Suppose Mika has budget of $600 for only two goods, x and y. The price of a Good X is $10 and the price of good Y is $25. Mika's utility function for Good x and Good y is: U(x, y) = 2xy. Suppose the price of a Good X increases to $15. a. What is Mika's initial basket when the price of a Good X is $10? b. How much utility does this basket generate for Mika? c. What is Mika's final consumption basket when the price of Good X increases to $15?
Suppose Mika has budget of $600 for only two goods, x and y. The price of a Good X is $10 and the price of good Y is $25. Mika's utility function for Good x and Good y is: U(x, y) = 2xy. Suppose the price of a Good X increases to $15. a. What is Mika's initial basket when the price of a Good X is $10? b. How much utility does this basket generate for Mika? c. What is Mika's final consumption basket when the price of Good X increases to $15?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Utility Maximization Problem
Suppose Mika has a budget of $600 for only two goods, \( x \) and \( y \). The price of Good \( x \) is $10, and the price of Good \( y \) is $25. Mika’s utility function for Good \( x \) and Good \( y \) is: \( U(x, y) = 2xy \).
Suppose the price of Good \( x \) increases to $15.
#### Questions:
a. What is Mika’s initial basket when the price of Good \( x \) is $10?
b. How much utility does this basket generate for Mika?
c. What is Mika’s final consumption basket when the price of Good \( x \) increases to $15?
---
**Explanation:**
To solve this problem, we need to perform the following steps:
1. **Determine the initial quantities of Good \( x \) and Good \( y \) that maximize Mika's utility given her budget and initial prices.**
2. **Calculate the utility generated by this initial basket using the utility function \( U(x, y) = 2xy \).**
3. **Recalculate the optimal quantities of Good \( x \) and Good \( y \) after the price of Good \( x \) increases and compute the final consumption basket.**
**a. Initial Basket**
Initially, the prices of Good \( x \) and Good \( y \) are $10 and $25 respectively. The budget constraint is given by:
\[ 10x + 25y = 600 \]
To maximize the utility function:
\[ U(x, y) = 2xy \]
Given the budget constraint, solving the system of equations will provide the optimal quantities of \( x \) and \( y \).
**b. Utility Generated by Initial Basket**
Using the quantities of \( x \) and \( y \) derived from part (a), we can compute the utility generated by substituting these values into the utility function:
\[ U(x, y) = 2xy \]
**c. Final Consumption Basket**
After the price of Good \( x \) increases to $15, the new budget constraint becomes:
\[ 15x + 25y = 600 \]
Again, we need to determine the new optimal quantities of \( x \) and \( y \) that maximize Mika's utility given the updated budget constraint and compute the final](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d4388d9-d500-459f-b12d-572cf956448e%2F2c10cd2c-35aa-474a-9219-9f2ba0268058%2F8yg0xb_processed.png&w=3840&q=75)
Transcribed Image Text:### Utility Maximization Problem
Suppose Mika has a budget of $600 for only two goods, \( x \) and \( y \). The price of Good \( x \) is $10, and the price of Good \( y \) is $25. Mika’s utility function for Good \( x \) and Good \( y \) is: \( U(x, y) = 2xy \).
Suppose the price of Good \( x \) increases to $15.
#### Questions:
a. What is Mika’s initial basket when the price of Good \( x \) is $10?
b. How much utility does this basket generate for Mika?
c. What is Mika’s final consumption basket when the price of Good \( x \) increases to $15?
---
**Explanation:**
To solve this problem, we need to perform the following steps:
1. **Determine the initial quantities of Good \( x \) and Good \( y \) that maximize Mika's utility given her budget and initial prices.**
2. **Calculate the utility generated by this initial basket using the utility function \( U(x, y) = 2xy \).**
3. **Recalculate the optimal quantities of Good \( x \) and Good \( y \) after the price of Good \( x \) increases and compute the final consumption basket.**
**a. Initial Basket**
Initially, the prices of Good \( x \) and Good \( y \) are $10 and $25 respectively. The budget constraint is given by:
\[ 10x + 25y = 600 \]
To maximize the utility function:
\[ U(x, y) = 2xy \]
Given the budget constraint, solving the system of equations will provide the optimal quantities of \( x \) and \( y \).
**b. Utility Generated by Initial Basket**
Using the quantities of \( x \) and \( y \) derived from part (a), we can compute the utility generated by substituting these values into the utility function:
\[ U(x, y) = 2xy \]
**c. Final Consumption Basket**
After the price of Good \( x \) increases to $15, the new budget constraint becomes:
\[ 15x + 25y = 600 \]
Again, we need to determine the new optimal quantities of \( x \) and \( y \) that maximize Mika's utility given the updated budget constraint and compute the final
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