CONDITIONS FOR CONSUMER EQUILIBRIUM FOR ONE GOODS, TWO GOODS AND MULTIPLE GOODS

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Every consumer has one goal in mind, which is to maximize utility given his limited budget. This is the reason for today's topic: Consumer equilibrium.

Consumer equilibrium can be defined as a state whereby a consumer allocates his money income in such a way that gives him maximum satisfaction given his income and has no tendency to change his consumption pattern.

In other words, consumer equilibrium refers to a situation where the consumer gets the maximum satisfaction such that he does not consider changing his consumption.

Condition of Consumer equilibrium for a single commodity

In the case of a single good, let's call it good X, the consumer is in equilibrium when the price of the last unit spent on good X equals the marginal utility of the last unit.

In other words, the condition of consumer equilibrium for one good, say good X, is that the marginal utility of good X ($MU_X$) should be equal to the price of X ($P_X$) paid for good X.

To represent this symbolically, a consumer is at equilibrium where:

$$MU_x=P_x$$

What happens when marginal utility is greater than price?

When marginal utility is greater than price, the consumer is in disequilibrium such that the consumer can only maximize his utility by purchasing more units of goods X.

As the consumer buys more of goods X, the marginal utility diminishes until it equals price so that the consumer is at equilibrium.

What happens when marginal utility is lesser than price?

When marginal utility is lesser than price, the consumer is at disequilibrium such that the consumer can only maximize his utility by purchasing fewer units of goods Y.

Consumer equilibrium for multiple goods

In the case of multiple goods, the consumer is at equilibrium where marginal utility derived from the last dollar spent on each good is identical.

In other words, for multiple goods, the consumer will be in equilibrium where the ratio of marginal utility of each commodity to their prices is similar.

That is, the consumer will be in equilibrium where:

$$\frac{MU_x}{P_x}=\frac{MU_y}{P_x}=............=\frac{MU_n}{P_n}$$

Consumer equilibrium for two goods using the indifference curve and budget line method

A consumer will be at equilibrium where the budget line is tangent to the indifference curve such that the slope of the budget line is equal to the slope of the indifference curve.

The slope of the indifference curve for two goods, say X and Y, shows the marginal rate of substitution of  X and Y. 

The slope of the budget line for goods X and Y shows the relative of goods X and Y. Given this, we can conclude that a consumer maximizes equilibrium where:

$$\frac{P_X}{P_Y}=MRS_{XY}$$

In summary, a consumer will be in equilibrium if and only if:

1. Marginal utility of the last naira spent on the goods is equal to the price in the case of one good.

2. Marginal utility derived from the last dollar spent on each good is identical in the case of multiple goods.

3. The budget line is tangent to the indifference curve.

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