EC2066: Jo Spends her Income on Clothes (X) and a Composite of all Other Goods (Y): Microeconomics Assignment, UOL, Singapore

1. Jo spends her income on clothes (X) and a composite of all other goods (Y). Her preferences are represented by the utility function
𝑢(𝑋, 𝑌) = √𝑋 + 𝑌/2
The price of the composite good is 1, and the price of the clothes is p. Let M denote Jo’s income.

a) Derive Jo’s demand for X and Y.
b) Suppose M = 10. Suppose initially the price of X is 1/2, and then the price falls
to 1/6. How much does Jo’s demand for X change? How much of this change in
demand can be attributed to income effect and how much to substitution effect?
c) Consider the change in price of X from 1/2 to 1/6. Calculate the compensating variation of the price change.
d) Consider the change in price of X from 1/2 to 1/6. Calculate the equivalent
variation of the price change.

2.Andy purchases only two goods, apples (A) and oranges (R). The price of
apples is 2 and the price of oranges is 4. Andy has an income of 40 and his utility function is
u(A, R) = 3A + 5R
What bundle of apples and oranges should Andy purchase to maximize utility?