1. (1) Suppose u = x1x2 , (x1 , x2 )∈ R2+ ，find the expenditure function e (p1, p2, u), that
corresponds to the utility function.

(2) Suppose u’= lnx1 + lnx2 , (x1 , x2 )∈ R2+ ，find the expenditure function e’ (p1, p2,
u’), that corresponds to the utility function.

2. Lily’s utility function is U(X, Y) =X2Y3, where X and Y represent the quantities of the
only two goods Lily consumes. The prices of the two goods are px=\$2 and py=\$6. Lily’s
income is \$1,000 per month.

(a) Find the quantities of X and Y Lily would consume in order to maximize her utility.

(b) Suppose py goes up to \$10. What will now be the utility maximizing quantities of
consumption?

(c) Find the compensating variation of this price change.

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