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 p = 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 r 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] Now consider only the restricted case (i.c., certificate can only be spent on good x). (iii) Someone offers to buy the gift certificate. Let $M be the minimum amount of money the individual will accept to sell it. What is M? (You may round off your answer to 2 decimal places)
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 p = 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 r 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] Now consider only the restricted case (i.c., certificate can only be spent on good x). (iii) Someone offers to buy the gift certificate. Let $M be the minimum amount of money the individual will accept to sell it. What is M? (You may round off your answer to 2 decimal places)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Only part (iii) please, thank you!
![**Problem 1: Consumer Choice with Gift Certificate**
An individual consumes two goods, \(x\) and \(y\). Her utility function is given by:
\[ U(x, y) = x^{1/3} y^{2/3} \]
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. Determine her optimal bundle.
**(ii) (Restricted)**
Now find her utility-maximizing bundle if the gift certificate is restricted to be spent on only good \(x\). Consider the amount she spends on \(x\) in the unrestricted case from part (i).
Now focus only on the restricted case (i.e., the certificate can only be spent on good \(x\)).
**(iii)**
Someone offers to buy the gift certificate. Let \(\$M\) be the minimum amount of money the individual will accept to sell it. Determine the value of \(M\). (You may round off your answer to 2 decimal places.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3585354-64d7-4f4a-b055-4a9b75b3799d%2F288d6800-1254-490a-82b4-6d7f4869c03a%2Fzi6a9su_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 1: Consumer Choice with Gift Certificate**
An individual consumes two goods, \(x\) and \(y\). Her utility function is given by:
\[ U(x, y) = x^{1/3} y^{2/3} \]
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. Determine her optimal bundle.
**(ii) (Restricted)**
Now find her utility-maximizing bundle if the gift certificate is restricted to be spent on only good \(x\). Consider the amount she spends on \(x\) in the unrestricted case from part (i).
Now focus only on the restricted case (i.e., the certificate can only be spent on good \(x\)).
**(iii)**
Someone offers to buy the gift certificate. Let \(\$M\) be the minimum amount of money the individual will accept to sell it. Determine the value of \(M\). (You may round off your answer to 2 decimal places.)
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