2 Important Conditions that must be satisfied for Consumer Equilibrium

Indifference map shows the tastes and preferences of the consumer independently of the market conditions, i.e., what the consumer would like to do.

On the other hand, the budget line represents the purchasing power or opportunities open to the consumer in the market, given his income and prices of the commodities, i.e., what the consumer is able to do.

The indifference map and the budget line are quite independent of each other so long as the consumer does not start making purchases in the market.

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However, both of these instruments are important in the determination of consumer equilibrium or in predicting what consumer will actually do, i.e., how the consumer spends his money in the pursuit of his needs and interests.

Every consumer wants to maximise the satisfaction. But, income constraint sets limits to his maximizing behaviour. The consumer who wants to get the most for his income would like to land on as high an indifference curve as his purchasing power permits, i.e., the highest indifference curve which can be reached from his budget line.

To get the consumer’s equilibrium, the budget line is super- imposed upon the indifference map.

Consumer is said to be in equilibrium, where he maximises the satisfaction, subject to his budget or income constraint. Consumer equilibrium is graphically illustrated in Fig. 5.21(a). In this figure, AB is the budget line. Consumer can choose any combination of commodities ‘X’ and ‘Y’.

Four indifference curves IC₁, IC₂, IC₃ and IC₄, out of the indifference map of the consumer are also shown in this diagram. All combinations of the commodities beyond the budget line and hence indifference curves IC₃ and IC₄, are not within the reach of the consumer.

He would not like to choose a combination below this budget line, as it will not give maximum possible satisfaction to the consumer. Therefore, in any case, consumer equilibrium must lie on the budget line. But, ‘C’ and ‘D’ points on the budget line will not ensure maximum possible satisfaction to the consumer, since these points lie on a lower indifference curve IC₁ and it is possible to reach a combination of commodities on a higher indifference curve IC₂ with the same money income.

Indifference curve IC₂ is the highest indifference curve that the consumer can reach, given his budget constraint. The budget line touches this indifference curve 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’ lie on lower indifference curves and thus indicate a lower level of satisfaction .Thus, given the budget constraint, the consumer maximises his satisfaction at the point, where his budget line is tangential to an indifference curve.

The budget line can be tangent to one and only one indifference curve. If we draw a budget line, which is tangent to two or more indifference curves, it would necessitate intersection of the curve, which is against the properties of indifference curves.

The two conditions of consumer equilibrium are:

(a) First Order Condition:

Since at the point of equilibrium, budget line is tangent to the indifference curve, so the slope of the budget line should be equal to the slope of the indifference curve and both the slopes are negative. Thus,

P_x/P_y = MRS_X,Y ….(5.3)

Or, the ratio of prices between the two goods is equal to the marginal rate of substitution of commodity ‘X’ for commodity ‘ Y’. The implication is that, at equilibrium, the rate at which the consumer can exchange ‘X’ for ‘Y’ (or, P_x/P_y) should be equal to the rate at which he is willing to substitute ‘X’ for ‘Y’ (i.e., MRS_{X y}). Since MRS_{X y}= MU_x/MU_y, we can write equation (5.3) as

P_x/P_y = MU_X/MU_Y

Or MU_X/MU_Y = P_x/P_y

This implies that at the point of equilibrium, the marginal utilities of the two commodities are proportional to their respective prices. The above equation (5.4) is same as we got under the law of equi-marginal utility, discussed.

This implies that a rational consumer can maximise his utility by allocating his income between the two commodities in such a manner that the marginal utility per rupee spent on commodity ‘X’ equals the marginal utility per rupee spent on commodity ‘Y’ In other words, the marginal utility per rupee spent on each commodity must be the same at equilibrium.

(b) Second Order Condition:

At the point of consumer equilibrium, indifference curve is convex to the origin, i.e., MRS is diminishing. If the indifference curve is not convex to the origin at the point where the price line is tangential to the indifference curve, the consumer equilibrium will not be stable. In Fig. 5.21(b), the indifference curve touches the budget line at point ‘P’.

Here, only the first order condition of consumer equilibrium is satisfied. But, the indifference curve is concave at the point of contact. The marginal rate of substitution is increasing at this point ‘P’.

Hence, the movement away from this point towards either side of the budget line may lead the consumer to a higher indifference curve. Point ‘Q’ on the indifference curve is in fact the point of maximum satisfaction and of stable equilibrium.