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For a consumer to be in equilibrium why must marginal rate of substitution be equal to the ratio of prices of the two goods? |
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Answer» Solution :(i) To define consumer equilibrium, we use Interference Curve map and the BUDGET line . Two conditions for consumer Equilibrium (a) NECESSARY Condition Marginal Rate of Substitution = Market Rate of Exchange `[(P_x)/(P_y)]` Or , `MRS_(x,y)=P_x//P_y` ( Market Rate of Exchange ) MRE Or `MRS_(x,y) =MRE[(P_x)/P_y]` `"*" ` If `MRS_(x,y) gt MRE [(P_x)/(P_y)]` , At point T in FIGURE It means the consumer.s willingness to pay for commodity X is higher than what makes values for commodity X. So, the consumer should buy more of X and less of Y to get MRS `=P_x/P_y`  `"*"` If `MRS_(x,y) lt MRE [(P_x)/(P_y)]`, At point W in figure, It means the consumer willingness to pay for commodity X is lesser than what market value for commodity X ,So, consumer should buy less of X and more Y to get MRS = `p_x/p_y` (b) Sufficient Condition `MRS_(x,y)` Diminishing (Convex) at a point of equilibrium i.e., when `MRS_(xy)=MRE[P_x/P_y]` (II) The consumer will reach equilibrium when the budget line is tangential to the higher possible Indifference Curve, i.e. ., where necessary and sufficient condition satisfy . In the above diagram , the consumer will reach equilibrium at point E where budget line RS is tangential to the higher possible `IC_2` (iii) The consumer cannot move to Indifference Curve , i.e. ., `IC _3`as this is beyond this money income. (iv) EVEN on `IC_2` all the other points except E are beyond his means . (v) Hence , at point E, the consumer is in equilibrium where his satisfaction maximizes, given his income and prices of goods X and Y . In equilibrium at E , the slope of Budget line = the slope of Indifference Curve. Therefore `MRS_(xy)`is equal to the ratio of the price bof two goods `[(P_x)/(P_y)]` . |
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