A consumer’s utility function is given by the expression:  ( ) 2 0.5 0.5 U = 0.6X + 0.4Y .  • Determine the marginal utility functions for each commodity.  Does marginal utility decrease when consumption increases? • Assuming that the price of good X is Rs 15 and the price of  Y is Rs 6, write the equation of the budget line and plot it  when income is Rs 450. What is its slope? What does it  indicate? • Calculate the marginal rate of substitution of Y for X and  interpret its economic meaning. Write the equation showing  consumer’s equilibrium condition.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.13P
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A consumer’s utility function is given by the expression: 
( )
2 0.5 0.5 U = 0.6X + 0.4Y . 
• Determine the marginal utility functions for each commodity. 
Does marginal utility decrease when consumption increases?
• Assuming that the price of good X is Rs 15 and the price of 
Y is Rs 6, write the equation of the budget line and plot it 
when income is Rs 450. What is its slope? What does it 
indicate?
• Calculate the marginal rate of substitution of Y for X and 
interpret its economic meaning. Write the equation showing 
consumer’s equilibrium condition. 
• Obtain the equilibrium values of X and Y. 
• Find the expressions for change in MUX due to increase in Y 
and change in MUY due to increase in X

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