Question

A consumer consumes only two goods X and Y, and is in equilibrium. Show that when the price of good X rises, the consumer buys less of good X. Use the utility analysis.

Answer 1

In case of two commodities, say X and Y, consumer's equilibrium is attained when,

$\frac{M{U}_X}{P_X}=\frac{M{U}_Y}{P_Y}$

But, when price of good X rises,

$\frac{M{U}_X}{P_X}<\frac{M{U}_Y}{P_Y}$

which shows that rupee worth of satisfaction is less for X than for Y. Since X is now relatively expensive when compared to Y, the consumer will start consuming less of X and more of Y. As a consequence, $\frac{M{U}_Y}{P_Y}$ will start falling while $\frac{M{U}_X}{P_X}$ will start rising. The consumer will start buying more of X when,

$\frac{M{U}_X}{P_X}=\frac{M{U}_Y}{P_Y}$

Thus, when price of good X rises, demand for the same falls, assuming price of Y and income of the consumer is constant.