Question

A consumer consumes only two goods X and Y and is in equilibrium. Price of X falls. Explain the reaction of the consumer through the Utility Analysis.

Answer 1

In case of two commodities, the consumer’s equilibrium is attained at that point, where; the utility derived from each additional unit of the rupee spent on each of the commodities is equal. That is, Marginal Utility of a Rupee spent on the commodity `x(i.e (MU_x)/(P_x))` is equal to the Marginal Utility of a Rupee spent on the commodity `Y(i.e (MU_y)/(P_y))`which in turn is equal to the Marginal Utility of Money (MU_m). That is, 

`    (MU_x)/(P_x)     (MU_y)/(P_y)=MU_m` 

If price of the commodity X falls, then the value of the fraction `((MU_x)/(P_x))`increases. Mathematically, this implies: 

`(MU_x)/(P_x)>(MU_y)/(P_y)=MU_m`

In such a situation, the consumer would increase his consumption of commodity X. He will continue to increase the consumption of commodity X until the equality between the marginal utilities of each of the commodities become equal to the marginal utility of money. At this situation, the equilibrium is restored. That is, 

`(MU_x)/(P_x)=(MU_y)/(P_y)=MU_m`