Question

1) Explain the relationship between total utility, marginal utility, and average utility.

2) What is consumer optimum?

3) How do you calculate consumer optimum?

Answer 1

1. There are three types of Utility:

• Total Utility
• Marginal Utility
• Average Utility

Total Utility : The utility which a consumer obtains by consuming all units of a commodity in a particular period of time is called total utility.

Total Utility = (Utility derived from unit 1 + Utility derived from Unit 2 + ------------- Utility derived from Unit n)

TU = (Un_{, +} Un_{2 + -----------------} Un_n)

Margin Utility : The utility which consumer obtains by consuming extra unit of a commodity is called marginal utility. Marginal Utility is the change in total utility due to change in unit of consumption of commodity.

Margin Utility = Change in total Utility/ Change in unit of consumption of commodity.

Average Utility As the name suggests it is the total utility divided by the units of commodity consumed.

Average Utility = Total Utility / Units of Commodity Consumed.

It is satisfaction enjoyed by the consumer from per unit commodity consumed.

Relation between Total Utility , Marginal Utility and Average Utility

• Total Utility is sum total of Marginal Utility and Marginal Utility is change in Total Utility.
• Total Utility is always positive but Marginal Utility may be positive, negative or even zero.
• When Marginal Utility is positive, Total Utility increases at diminishing rate.
• When Marginal Utility is zero, Total Utility is maximum.
• When Marginal Utility is negative, Total Utility is declining.
• Average Utility is always positive.
• When Average Utility attains maximum value, it is equal to Marginal Utility.

2. Consumer Optimum

A consumer optimum represents a solution to a problem facing all individuals -- maximizing the satisfaction (utility) from consuming different goods and services subject to the constraint of household income and product prices. So, we can say Consumer optimum is a choice of a set of goods and services that maximizes the utility of each consumer, subject to limited income. This optimum is reached when the marginal utility of the last dollar spent on each good yields the same utility and all income is spent.

Consumer Optimum in case of consumption of one good

Consumer optimum in consumption of one good

Suppose that a consumer consumes only one good and we are looking for optimal quantity of this good, i.e. quantity which consumption will maximize utility of consumer. Finding of the consumer's optimum is based on the assumption that consumer will be willing to pay the asked price for the good only as long as he/she will attribute greater or equal utility to each unit of consumed good (i.e. until MU≥p). He/she will stop his/her consumption (will buy the last good) when the utility of the good will be equal to the price.

Consumer optimum in consumption of two or more goods

If the consumer consumes more goods, then the marginal utility function from consumption of each of them can be obtained  by the partial derivation of the total utility function according to amount of the corresponding good.

3. Formula for Consumer Optimum

Maximizing Total Utility

MU A/Price A = MU B/Price B = MU C/Price C = MU N/Price N

Where A,B and C represents three different goods and MU = Marginal Utility