### Utility Maximization ProblemSuppose 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

The ability of a good to fulfill human needs is demonstrated by its utility. The utility function…

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?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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