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A consumer consumer 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 utility analysis. |
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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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