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Derive the law of demand from the two commodity equilibrium condition " Marginal Utility = price ratio through utility approach''. |
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Answer» Solution :(i) The law states that a consumer is in equilibrium when the ratio of MU to price in CASE of each good consumed is the same. In of goods, X and Y , a consumer is in equilibrium when , `(MU_x)/P_x =(MU_y)/P_y` (ii) Given that the consumer is in equilibrium and price of X falls. It can be seen from the figure that figure B is derived from Figure A  (iii) In figure A, initially , the consumer equilibrium is attached at point E where `(MU_x)/(P_x)=(MU_y)/P_y`(Assuming, `P_x=10`) Corresponding to point E , we derive point E, in figure B . (iv) DUE to FALL in price (suppose from 10 to 8),`(MU_x)/(P_x)gt(MU_y)/P_y`at the given QUANTITY Q . It means , marginal utility from the last rupee spent on commodity X is more than marginal utility from the last rupees spent on commodity Y . So , to attain the equilibrium the consumer must increase the quantity of X , which decreases the `MU_x` and decreases the `MU_y`Increase in quantity of Y continue till`(MU_x)/(P_x)= (MU_y)/P_y`and the new consumer equilibrium will be attached at point F. Corresponding to point F ,we derive the point `F_1` in figure B, So , by JOINING point `E_1 and F_1`. we derive the demand curve . |
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