Question

Explain consumer's equilibrium in case of a single commodity in terms cardinal utility theory.

Answer 1

Initially, we illustrate consumer's equilibrium by taking a simple one commodity case. Suppose that a consumer with certain given money income consumes only one commodity, X. The relevant question here is how much quantity of X should the consumer purchase at its given price so as to reach the equilibrium? The simple answer to this is that the consumer should purchase that much quantity of the commodity at its given price, given his income, so that he can maximise the total utility from his purchase.

A utility-maximising consumer will be in equilibrium when he purchases that much quantity of the commodity where the marginal utility of the commodity equals its price. 

Since money (price) which the consumer has to spend to purchase a unit of the commodity and the commodity both gives him utility, he can either spend the money (income) on the purchase of the commodity or keep it with himself. If marginal utility of a commodity is greater than the marginal utility of money which the consumer has to give to purchase the commodity, a utility-maximising consumer will purchase the commodity in exchange for money, i.e., the consumer can increase total utility by purchasing more units of the commodity at its lower price. Thus, if marginal utility of X is greater than the price of X (i.e., MU_x > P_x), the consumer can increase his total utility by purchasing more units of X. Likewise, if marginal utility of X is less than its price (i.e., MU_x < P_x), the consumer can increase his total utility by consuming less units of X. He will maximise total utility when marginal utility of a commodity equals its price.

Symbolically, consumer's equilibrium is attained when

MU_x = P_x

where MU_x is Marginal utility of commodity X, P_x shows price of commodity X.

Units of Shirt	Marginal Utility (in ₹)
1	700
2	650
3	600
4	500
5	350

Consumer's equilibrium in a single commodity case is illustrated by a numerical example in Table and in diagram. Suppose the consumer wants to purchase shirts. He gets utility (measured in terms of money) from different units of shirt as indicated in Table. It is obvious from Table that the consumer gets marginal utility equal to ₹ 700 from the first shirt. As he consumes (buys) additional units of shirt, the marginal utility goes on diminishing. Price of the shirt is assumed to be ₹ 600. The consumer will be in equilibrium when he purchases 3 shirts because the marginal utility of third shirt (₹ 600) is equal to the price of the shirt (₹ 600).

In diagram, MU curve is the marginal utility curve of shirts expressed in terms of money. The downward sloping MU curve indicates the law of diminishing marginal utility. The horizontal line P shows the price of a shirt. The MU curve and price line P intersect each other at point E. Therefore, the consumer is in equilibrium at point E, where the MU = P.

In our example, this condition is satisfied when he purchases 3 shirts. At any point above E, MU > P. For instance, the 2nd shirt gives him satisfaction equal to ₹ 650, while the price of the shirt is ₹ 600. Therefore, the consumer can increase his total utility by purchasing 2nd shirt. Likewise, at any point below E, MU < P. The consumer can, therefore, increase his satisfaction by reducing his purchase. For instance, the consumer will not like to purchase the 4th shirt because it gives him utility equal to ₹ 500, which is less than the price of the shirt (₹ 600). Thus, point E is the point of equilibrium where MU of shirt is equal to the price of the shirt.

Thus, the consumer will be maximising total utility while purchasing a commodity, i.e., he will be in equilibrium, when he equalises the marginal utility he gets from a commodity with its price.