Explain the conditions of consumer's equilibrium under utility analysis

Explanation

Conditions for consumer's equilibrium are:
(i) Budget line should be tangent to indifference curve, i.e.,
`MRS_(xy) = (P_(x))/(P_(y))`
(Slope of IC) = Slope of Budget Line
(ii) Indifference curve should be convex to the point of origin, i.e., MRS is diminishing.
At equilibrium, marginal rate of substitution should be equal to the ratio of prices of the two goods:
`MRS_(xy) gt P_(x)//P_(y)`. It means that to obtain one extra unit of X the consumer is willing to sacrifice more than he has to sacrifice actually. In the process, 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 sacrifice less and less of Y each time he obtains one extra unit of X. As a result, `MRS_(xy)` falls and ultimately becomes equal to `P_(x)//P_(y)` at some combination of X and Y. At this combination the consumer is in equilibrium.
`MRS_(xy) lt P_(x)//P_(y)`. 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 he will start losing. So he will not try to obtain more of X.