Answer to Question #174926 in Microeconomics for John

Question

Prove that the utility approach and the indifference-curve approach yield

the same consumer equilibrium. Consider two goods, A and B, to explain

the utility approach and the indifference curve approach

Answer 1

UTILITY APPROACH

Consumer equilibrium is achieved when the consumer maximizes their satisfaction by utilizing their income on various goods and services. When changes are made on income allocation for the different goods, total satisfaction falls.

In the case of two commodities say A and B, marginal utility of money must be the same across both good A and B, and should also be equal to the Rupee (currency) worth of marginal utility of money.

MU(of good A)/ Price of good A = MU(OF GOOD B)/ Price of good B = MU(of money) 

This is because incase rupee worth of satisfaction is less for good B and greater for good A, it means that the consumer will purchase more of good A and less of good B. this will lead to a fall in marginal utility of good A and a rise in marginal utility of good Y.

INDIFFERENCE CURVE APPROACH

Equilibrium of the consumer refers to the choice of the bundle of goods that maximize utility.

An indifference curve shows combination of two goods that yield equal satisfaction and utility to the consumer. Different points point on an indifference curve clearly shows that the consumer is indifferent between the two points but all points yield the same utility.