A consumer consumer only two goods. For the consumer to be in equilibrium, why must Marginal Rate of Substitution between the two goods must be equal to the ratio of prices of these two goods ? Is it enough to ensure equilibrium ?

A consumer consumer only two goods. For the consumer to be in equilibr

1.	A consumer consumer only two goods. For the consumer to be in equilibrium, why must Marginal Rate of Substitution between the two goods must be equal to the ratio of prices of these two goods ? Is it enough to ensure equilibrium ?
Answer» <P> Solution :Let the two goods be X and Y. `MRS_(XY)` is the number of units of Y the consumer is willing to sacrifice to obtain one extra unit of X. The ration of prices is `P_(X)//P_(Y)` which also equals the ratio of the number of units of Y required to be sacrificed to obtain one extra unit of X in the market. Initially, when the consumer starts purchases, `MRS_(XY)` is greater than `P_(X)//P_(Y)`. It means that to obtainone extra unit of X, the consumer is willing to sacrifice more than he has to sacrifice actually. The consumer gains. As he GOES on obtaining more and more units of X, marginal utility of X goes on declining. Therefore, the consumer is willing to sacrifices LESS and less of Y each time he OBTAINS one extra unit of X. As a result, `MRS_(XY)` falls and ULTIMATELY become equal to `P_(X)//P_(Y)` at some combination of X and Y. At this combination, the consumer is in equilibrium. If the consumer attempts to obtain more units of X beyond the equilibrium level, `MRS_(XY)` will become less than `P_(X)//P_(Y)` and his total utility will start falling. So, he will not try to obtain more of X.