Do the demand functions derived in this example ensure that total spending on x and y will exhaust the individual’s income for any combination of p x , p y and I ? Can you prove that this is the case? Homogeneity of demand is a direct result of the utility-maximisation assumption. Demand functions derived from utility maximisation will be homogeneous and, conversely, demand functions that are not homogeneous cannot reflect utility maximisation (unless prices enter directly into the utility function itself, as they might for goods with snob appeal). If, for example, an individual’s utility for food (x) and housing (y) is given by utility = U(x, y) = x 0.3y 0.7, (5.4)

then it is a simple matter (following the procedure used in Example 4.1) to derive the demand functions x* =

0.3I px

, y* =

0.7I py

.

(5.5)

These functions obviously exhibit homogeneity because a doubling of all prices and income would leave x* and y*

unaffected.