4.12 In a two-commodity world a consumer's preferences are represented by the utility function
l
U(xl, x2) ax 2 + x2
where (xl, x2) represent the quantities consumed of the two goods and a is a non-negative parameter.
1. If the consumer's income y is fixed in money terms find the demand functions for both goods, the cost (expenditure) function and the indirect utility
function.
2. Show that, if both commodities are consumed in positive amounts, the
l
compensating variation for a change in the price of good 1 pl — pt is
given by
a2p2 r 1 1 l
2
p
4
l
t – pl
3. In this case, why is the compensating variation equal to the equivalent variation and consumer's surplus?
