A consumer consumes only two goods X and Y. At a consumption level of these two goods , he finds that the ratio of marginal utility to price in case of X is higher than that in case. of X is higher than that in case of Y . Explain the reaction of consumer.

Solution :As, we know conditions for consumer equilibrium is ,
Necessary Condition
Marginal UTILITY of last rupee spent on each commodity is same .
SUPPOSE there are two commodities, X and Y respectively.
So , for commodity X, the condition is, Marginal Utility of Money = Price of X
Or `(" Marginal in Util Product in Util " [MU_x])/( "Marginal Utility of One Rupee " [MU_R])` = Price of X
or `(MU_x)/(P_x) = MU_R "".....(1)`
Similarly, for commodity Y , the condition is,
`(MU_y)/P_y=MU_R ""....(2)`
Putting EQUATION (2) in (1), we get
`(MU_x)/(P_y)=(MU_y)/P_y`
But as given in the question that the ratio of marginal utility to price in CASE of X is HIGHER than that in case of Y, i.e., `(MU_x)/P_x gt (MU_y)/P_y`
It means marginal utility from the last rupee spent on commodity X is more than marginal utility from the last rupee spent on commodity Y. So, to attain the equilibrium consumer must increase the quantity of X, which decreases the `MU_x` and decreases the quantity of Y, which will increase the `MU_y` Increase in quantity of X and decrease in quantity of Y continue till `(MU_x)/P_x = (MU_y)/P_y` .