Explain with the help of an indifference curve analysis how a consumer reaches the highest level of satisfaction

Q. Explain with the help of an indifference curve analysis how a consumer reaches the highest level of satisfaction? (May’06, Nov’07 and Nov’10).

Consumer’s Equilibrium by Indifference Curve: Consumer equilibrium refers to a situation, in which a consumer derives maximum satisfaction, with no intention to change it and subject to given prices and his given income. The point of maximum satisfaction is achieved by studying indifference map and budget line together.
Conditions of Consumer’s Equilibrium: The consumer’s equilibrium under the indifference curve theory must meet the following two conditions:


(i) MRS_XY = Ratio of prices or P_X/P_Y
A) If MRS_XY > P_X/P_Y, it means that the consumer is willing to pay more for X than the price prevailing in the market. As a result, the consumer buys more of X. As a result, MRS falls till it becomes equal to the ratio of prices and the equilibrium is established.
B) If MRS_XY < P_X/P_Y, it means that the consumer is willing to pay less for X than the price prevailing in the market. It induces the consumer to buys less of X and more of Y. As a result, MRS rises till it becomes equal to the ratio of prices and the equilibrium is established.

(ii) MRS continuously falls: The second condition for consumer’s equilibrium is that MRS must be diminishing at the point of equilibrium, i.e. the indifference curve must be convex to the origin at the point of equilibrium. Unless MRS continuously falls, the equilibrium cannot be established.
Let us now understand this with the help of a diagram:  
(i) MRS = Ratio of prices or P_X/P_Y:
(ii) MRS continuously falls:

Let the two goods be X and Y. The first condition for consumer’s equilibrium is that

MRS_XY = P_X/P_Y

Thus, both the conditions need to be fulfilled for a consumer to be in equilibrium.

In Fig. 2.12, IC₁, IC₂ and IC₃ are the three indifference curves and AB is the budget line. With the constraint of budget line, the highest indifference curve, which a consumer can reach, is IC₂. The budget line is tangent to indifference curve IC₂ at point ‘E’. This is the point of consumer equilibrium, where the consumer purchases OM quantity of commodity ‘X’ and ON quantity of commodity ‘Y.

All other points on the budget line to the left or right of point ‘E’ will lie on lower indifference curves and thus indicate a lower level of satisfaction. As budget line can be tangent to one and only one indifference curve, consumer maximizes his satisfaction at point E, when both the conditions of consumer’s equilibrium are satisfied:

At tangency point E, the absolute value of the slope of the indifference curve (MRS between X and Y) and that of the budget line (price ratio) are same. Equilibrium cannot be established at any other point as MRS_XY > P_X/P_Y at all points to the left of point E and MRS_XY < P_X/P_Y at all points to the right of point E. So, equilibrium is established at point E, when MRS_XY = P_X/P_Y.

The second condition is also satisfied at point E as MRS is diminishing at point E, i.e. IC₂ is convex to the origin at point E.