1. Consider an individual who consumes two goods, x and y. Her utility function is U(x, y) = x¹/³y2/3 The prices of the goods are p₁ = Py = 1. She has a gift certificate worth $40 and an income of I = $50. (i) (Unrestricted) Suppose the gift certificate is unrestricted so it can be spent on either or y or both. What is her optimal bundle?
1. Consider an individual who consumes two goods, x and y. Her utility function is U(x, y) = x¹/³y2/3 The prices of the goods are p₁ = Py = 1. She has a gift certificate worth $40 and an income of I = $50. (i) (Unrestricted) Suppose the gift certificate is unrestricted so it can be spent on either or y or both. What is her optimal bundle?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Only part (ii) please, thank you!
![**Problem Statement:**
1. Consider an individual who consumes two goods, \( x \) and \( y \). Her utility function is
\[
U(x, y) = x^{1/3}y^{2/3}
\]
The prices of the goods are \( p_x = p_y = 1 \). She has a gift certificate worth $40 and an income of \( I = \$50 \).
**(i) (Unrestricted)**
Suppose the gift certificate is *unrestricted* so it can be spent on either \( x \) or \( y \) or both. What is her optimal bundle?
**(ii) (Restricted)**
Now find her utility-maximizing bundle if the gift certificate is *restricted* to be spent on only good \( x \). [Think carefully. Take into account what she spends on \( x \) in (a), unrestricted case]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3585354-64d7-4f4a-b055-4a9b75b3799d%2F287b4c3b-fce8-46b1-bb10-443a7f7d0ebb%2Fps630j8_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
1. Consider an individual who consumes two goods, \( x \) and \( y \). Her utility function is
\[
U(x, y) = x^{1/3}y^{2/3}
\]
The prices of the goods are \( p_x = p_y = 1 \). She has a gift certificate worth $40 and an income of \( I = \$50 \).
**(i) (Unrestricted)**
Suppose the gift certificate is *unrestricted* so it can be spent on either \( x \) or \( y \) or both. What is her optimal bundle?
**(ii) (Restricted)**
Now find her utility-maximizing bundle if the gift certificate is *restricted* to be spent on only good \( x \). [Think carefully. Take into account what she spends on \( x \) in (a), unrestricted case]
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