Utility: Total and Marginal

Utility: total and marginal. Behind the demand curve lies the theory of consumer choice. Why do consumers purchase exactly as much as they do? The answer is connected to the concept of utility — the satisfaction a consumer receives from consuming goods.

Concept of Utility
Utility — a measure of satisfaction that a consumer obtains from consuming goods and services. It is a subjective concept — different people have different preferences.

Historical perspective: early economists (Jevons, Menger, Walras) assumed that utility is quantitatively measurable — in “utils.” Modern theory uses ordinal utility — only the order of preferences matters, not absolute values.

Cardinal utility: utility is measurable in units. “An apple provides 10 utils, a banana — 8.” Ordinal utility: only the order matters. “An apple is preferred to a banana.” One does not need to know “by how much.” Modern microeconomics uses the ordinal approach, but the cardinal model is useful for intuition.

Total and Marginal Utility
Total utility (TU) — the total satisfaction from consuming a certain quantity of a good. Marginal utility (MU) — the additional satisfaction from consuming one more unit.

$ MU = \Delta TU / \Delta Q = \frac{dTU}{dQ} $

Connection: TU — the sum (integral) of all MUs. MU — the derivative of TU.

Law of Diminishing Marginal Utility
Law of Diminishing Marginal Utility: as consumption of a good increases, the marginal utility of each additional unit decreases (all else equal).

Intuition:

• The first glass of water on a hot day — enormous utility
• The second — still good, but less
• The fifth — almost indifferent
• The tenth — might be unpleasant

Graphically:

• TU grows, but more slowly (convex curve)
• MU falls with each unit
• At some point, MU may become negative (oversaturation)

Important: the law applies to short-term consumption. Over the long term — habituation, changes in tastes — other effects.

Utility Maximization
The consumer maximizes utility under a budget constraint. How should income be allocated among goods?

Rule of equal marginal utility per unit of price:

$ \frac{MU_x}{P_x} = \frac{MU_y}{P_y} = ... = \lambda $

Where $\lambda$ is the marginal utility of income.

Intuition: the last ruble spent on any good should yield the same additional utility.

If $MU_x/P_x > MU_y/P_y$ — reallocate from Y to X, increasing total utility.

Deriving the demand curve:

• When $P_x$ falls, $MU_x/P_x$ rises
• To restore equality, one must increase consumption of X (reduce $MU_x$)
• Hence: lower price — higher consumption — the law of demand

Water and Diamond Paradox
Classic Adam Smith paradox: water is essential for life, but cheap. Diamonds — useless for survival, but expensive.

Resolution via marginal utility:

• Total utility of water is enormous — without it, one cannot survive
• Marginal utility of water is low — water is abundant, an extra liter adds almost nothing
• Marginal utility of diamonds is high — diamonds are scarce, each is valuable

Price is determined by marginal, not total utility.

Lesson: in economics, marginal values are important, not average or total.

Consumer Surplus
Consumer surplus — the difference between what a consumer is willing to pay and what they actually pay.

Connection to MU: willingness to pay per unit ≈ MU of that unit.

For the first units, consumers are willing to pay a lot (high MU), but the market price is the same for all units. The difference is the surplus.

Graphically: area between the demand curve and the price line.

Significance: consumer surplus is a measure of consumer welfare from participating in the market. Policies that reduce CS (taxes, restrictions) decrease welfare.

Limitations of Utility Theory
Behavioral deviations:

• People do not always maximize rationally
• Context effects, framing, mistakes

More details — in the behavioral economics module

Comparing utility between people:

• One cannot compare “my” and “your” utility
• This limits conclusions about redistribution

Dynamics of preferences:

• Tastes change over time
• Formation of habits, dependencies

Despite limitations, utility theory is a useful model for understanding consumer choice and forms the basis for the demand curve.