Question

A consumer consumes only two goods X and Y whose prices are Rs. 4 and Rs. 5 per unit respectively. If the consumer chooses a combination of the two goods with marginal utility of X equal to 5 and that of Y equal to 4, is the consumer in equilibrium? Give reasons. What will a rational consumer do in this situation? Use utility analysis.

Answer 1

Given, $P_X=Rs.4$; $P_Y=Rs.5$; $M{U}_X=Rs.5$; $M{U}_Y=4$

The consumer attains equilibrium when

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

In the given question, the consumer is not in the equilibrium because here,

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

Using the given values, $\frac{5}{4}>\frac{4}{5}$

The consumer would react to this situation by increasing the consumption of good X in place of good Y. As consumption of X is increased, $M{U}_X$ will start declining. Likewise, fall in the consumption of Y would cause a rise in $M{U}_Y$. The process of substituting X for Y would continue till $\frac{M{U}_X}{P_X}$ (rupee worth of $M{U}_X$) and $\frac{M{U}_Y}{P_Y}$ (rupee worth of $M{U}_Y$) are equal and the equilibrium is achieved.