Consumer’s equilibrium: utility approach

The essentials

Utility is the want-satisfying power of a commodity. In the cardinal utility approach it is measured in units called utils. Total utility (TU) is the total satisfaction from consuming a given quantity. Marginal utility (MU) is the change in total utility from consuming one more unit: MUn = TUn − TUn−1.

The law of diminishing marginal utility says that as a consumer takes more and more units of a good, the marginal utility from each successive unit goes on falling (other things constant). So TU rises at a falling rate, reaches its maximum when MU = 0, and falls when MU becomes negative.

Key points

• MU = ΔTU ÷ ΔQ; TU = sum of all marginal utilities.
• When MU is positive, TU increases; MU = 0 gives maximum TU; MU negative means TU falls.
• One-commodity equilibrium: the consumer buys good X until MUx ÷ Px = MUm, where MUm is the marginal utility of a rupee. Equivalently, MUx (in utils) = Px × MUm.
• Two-commodity equilibrium: MUx ÷ Px = MUy ÷ Py = MUm (law of equi-marginal utility). The last rupee spent on each good must give the same utility.
• If MUx ÷ Px > MUy ÷ Py, the consumer gains by shifting spending towards X. As more X is bought, MUx falls until the ratios become equal.
• The law of demand can be derived from this: when Px falls, MUx ÷ Px rises above MUm, so the consumer buys more X.

Exam tips

• In tables, compute MU column first, then compare MU with price × MUm.
• The consumer keeps buying as long as MU of the unit is at least equal to price × MUm.

Common mistakes

• Confusing "TU is maximum" with "MU is maximum". TU is maximum where MU is zero.
• Comparing MUx and MUy directly instead of MU per rupee (MU ÷ price).