Consumers Equilibrium Indifference Curve Approach

A consumer attains his equilibrium when he maximizes his total utility, given his income and the prices of the two commodities. We combine the indifference curve and the budget line to get consumer’s equilibrium.

Two condition is needed for the consumer to be in equilibrium.

1) MRS_xy = P_x/P_y

MRS_xy refers marginal rate of Substitution- It is the rate at which consumer is willing to substitute one good for another without changing the level of satisfaction.

For example: There are two commodities food(X) and clothing (Y).The marginal rate of Substitution X for Y is defined as the amount of X(food) the consumer is willing to give up to get one additional unit of Y(clothing) while maintaining the same level of satisfaction.

Given the amount of money which the consumer wants to spend on two commodities and given the prices of the two commodities, we can draw a budget line.

A budget line is a negatively sloping line as if a consumer wants to purchase more of one commodity, he has to sacrifice some amount of the other commodity. Its slope depends on the prices of the two commodities i.e. P_x/Py

Thus, the budget line shows the various combination which the consumer can afford to buy with his given budget and given prices of the two goods, the indifference map shows the consumer scale of preferences between various combinations of two goods.

2) The indifference curve should be convex to the origin- the slope of the curve decreases as we move down the curve. This is due to the assumption of diminishing Marginal Rate of Substitution.

This means that as the consumer substitutes more and more of one commodity say X for another commodity say Y, he will be prepared to give up lesser units of the Y for each additional units of X.

Explanation through the graph 

Consumers Equilibrium

As shown in the above diagram, two commodities food and clothing are taken and there various preferred combination are shown by the three indifference curves.

Budget line is shown by the straight, negatively sloped line.

The consumer cannot purchase any combination which lies to the right of the budget line, like combination ‘N’ as it is beyond his reach, with the given income.

Also any combination inside the budget line, like combination ‘M’ is within his reach but this will give him less utility as he will not be able to spend his entire income by choosing such a combination.

Thus, the combination of food and clothing with the highest utility must be on the budget line.

The highest indifference curve with a point on the budget line is the one that just touches (tangent) to the budget line. This occurs at point ‘T’

At this point OA amount of clothing and OB amount of food a consumer purchases, and the consumer is in equilibrium. This is the satiation point for him.

A rational consumer will not like to prefer IC₁, as it will give him less utility, so will not choose combination ‘M’. Point ‘N’ is preferred to point ‘T’, as it lies on higher indifference curve IC₃, but it is not feasible because it is outside the budget line. 

At point ‘T’, the slope of the indifference curve (MRSxy) between two goods and the slope of the budget line (Px/Py) are equal.

To conclude, a utility maximizing consumer, given his income, taste and preferences and prices of the two goods, will attain his equilibrium when marginal rate of substitution between two goods is equal to the price ratio of two commodities.