1.

By spending his entire income only on two goods X and Y a consumer finds that , (MU_x) /P_x lt (MU_y)/(P_y) . Explain how will the consumer reaction.

Answer»

Solution :As , we know condition for consumer equilibrium is ,
Necessary Condition
Marginal UTILITY of last rupeespend 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 Utility of a 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_x)=(MU_y)/P_y`
Putting equation (2) in (1), we get
`(MU_x)/P_x =(MU_y)/(P_y)`
But as given in the QUESTIONS that the ratio of marginal utility to price in case of X is lower than in case of Y.i.e, `(MU_x)/(P_x) lt (MU_y)/P_y` . It is means, marginal utility from the lest rupee spent on commodity X is less than the marginal utility from the last rupee spent on commodity Y . So, to attain the equilibrium the consumer must decrease the quantity of X which will increase the `MU_x` and increase the quantity of Y , which will decrease the `MU_y` . Decrease in quantity of X and increase in quantity of y continue TILL `(MU_x)/P_x =(MU_y)/(P_y)` .


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