A convex indifference curve exhibits a diminishing marginal rate of substitution. This is best described as:

A falling ratio of two marginal utilities along a curve of constant satisfaction

A falling marginal utility of each good individually

A falling total utility as consumption rises

A rising price ratio between the two goods

The Slutsky and Hicks decompositions of a price change differ chiefly in:

What is held constant while isolating the substitution effect — purchasing power (Slutsky) versus utility level (Hicks)

Whether the substitution effect can be positive

Whether the good is normal or inferior

Whether income is held constant in money terms

A Giffen good's demand curve slopes upward because:

Its negative income effect (it is inferior) outweighs the always-negative substitution effect

Its substitution effect is positive

Consumers have imperfect information about its price

It is a luxury good with high income elasticity

In the short run, the marginal cost curve intersects the average variable cost and average cost curves:

At their respective minimum points

At their respective maximum points

Returns to scale and the law of diminishing marginal returns differ chiefly because:

Returns to scale applies when all inputs vary together (long run); diminishing returns applies when only one input varies with others fixed (short run)

Returns to scale is a short-run concept and diminishing returns a long-run one

They are two names for the identical relationship

Returns to scale applies only to labour

A risk-averse agent's utility-of-wealth function is:

Concave, so the expected utility of a fair gamble is less than the utility of its expected value

Convex, so the agent prefers the gamble to its expected value

Linear, so the agent is indifferent between the gamble and its expected value

Undefined at any wealth level below the mean

Which of the following are properties of a well-behaved (standard) indifference curve?

A curve farther from the origin represents higher satisfaction

Two indifference curves for the same consumer can intersect

Consumer Behaviour, Production-Cost Theory and Decision-Making Under Uncertainty

Unit 1 opens the paper the way every microeconomics course opens — with the two decision-makers, the consumer and the firm — before moving to strategic interaction and market structure. This chapter covers consumer behaviour (utility, indifference curves, income-substitution effects, revealed preference), production and cost theory, and decision-making under uncertainty and risk; the next covers game theory, market structures and factor pricing; the third covers general equilibrium, efficiency criteria, welfare economics and asymmetric information.

1. Consumer Behaviour I: Indifference Curves and Consumer Equilibrium

The ordinal-utility approach represents preferences with indifference curves rather than a numerically measurable utility index: each curve joins bundles giving equal satisfaction, curves further from the origin represent higher satisfaction, and two indifference curves for the same consumer can never intersect — an intersection would imply the consumer is simultaneously indifferent and not indifferent between the same two bundles, violating transitivity. A well-behaved indifference curve is negatively sloped and convex to the origin. Consumer equilibrium under a budget constraint occurs where the indifference curve is tangent to the budget line — the marginal rate of substitution (MRS), the rate at which the consumer is willing to trade one good for another while holding satisfaction constant, equals the ratio of the two goods' prices (MRS = Px/Py).

Cardinal versus ordinal utility: what NET tests as the distinction
Approach	Core claim
Cardinal (Marshall)	Utility is measurable in numerical units (utils); the equilibrium condition is MUx/Px = MUy/Py — the law of equi-marginal utility.
Ordinal (Hicks-Allen)	Only ranking of bundles matters, not a numerical value; the equilibrium condition is MRS = Px/Py, derived without assuming utility is measurable.

⚠️ Diminishing MRS is not diminishing marginal utility

A convex indifference curve shows a diminishing marginal rate of substitution — as a consumer gives up more of good Y for equal increments of good X, they demand progressively less Y per additional unit of X. This is a statement about the RATIO of two marginal utilities changing along a curve of constant total satisfaction, not a claim that either good's own marginal utility is falling — ordinal theory does not need diminishing marginal utility of either good individually to derive a convex indifference curve.

2. Consumer Behaviour II: Income-Substitution Effects and Revealed Preference

A price fall changes quantity demanded through two channels that the Slutsky-Hicks decomposition separates. The substitution effect isolates the pure change in relative price by holding purchasing power (Slutsky) or utility (Hicks) constant — it is always negative: a fall in a good's own price, real income held fixed, never reduces its quantity demanded. The income effect captures the change in real purchasing power from the price fall and can be positive or negative depending on whether the good is normal (demand rises with income) or inferior (demand falls with income). A Giffen good is a special inferior good whose negative income effect is large enough to outweigh the substitution effect, so its own demand curve slopes upward — the one theoretical exception to the law of demand.

Normal good — income effect reinforces the substitution effect (both push demand the same direction as the price change would predict).
Inferior (non-Giffen) good — income effect opposes the substitution effect but is smaller, so the demand curve still slopes downward overall.
Giffen good — income effect opposes and dominates the substitution effect, producing an upward-sloping own demand curve.

🎯 Revealed preference sidesteps the utility function entirely

Samuelson's revealed preference theory derives consumer behaviour from observed choices alone, with no assumption about an underlying indifference map. The Weak Axiom of Revealed Preference (WARP) requires: if bundle A is chosen when bundle B was also affordable, then at any other prices/income where B is chosen, A must not be affordable — otherwise the consumer's choices are inconsistent. The Strong Axiom (SARP) extends this to chains of such comparisons, ruling out indirect inconsistency as well as direct.

3. Theory of Production and Costs

A production function Q = f(L, K) maps factor inputs to output; isoquants (equal-output curves) are the production analogue of indifference curves, convex to the origin, with slope equal to the marginal rate of technical substitution (MRTS = MPL/MPK), diminishing as more labour replaces capital. Returns to scale describe what happens when ALL inputs are scaled up together (increasing, constant or decreasing returns to scale), while the law of diminishing marginal returns describes the short run, where at least one factor is fixed — as more of the variable factor is added, its marginal product eventually falls. These are distinct concepts tested separately: returns to scale is a long-run, all-factors-variable idea, while diminishing returns is a short-run, one-factor-fixed idea.

Short-run cost curves and their U-shape
Curve	Behaviour
TFC, TVC, TC	Total fixed cost is constant with output; total variable cost rises, at a falling then rising rate (mirroring diminishing marginal returns); total cost is their sum.
MC, AVC, AC	MC (the slope of TVC/TC) is U-shaped and cuts both AVC and AC at their respective minimum points — a standard graph-reading question.

ℹ️ The long-run average cost curve is an envelope

With every factor variable in the long run, the LAC curve is the envelope of a family of short-run average cost (SAC) curves, one per plant size — it is tangent to (not generally passing through the minimum of) each SAC curve. Its own U-shape reflects economies of scale (falling LAC from specialisation, bulk purchasing) followed by diseconomies of scale (rising LAC from managerial/coordination difficulties), a distinct source from the short-run law of diminishing returns.

4. Decision-Making Under Uncertainty and Attitudes Towards Risk

The St. Petersburg paradox — a gamble with infinite expected monetary value that almost no one would pay much to play — shows that people do not simply maximise expected monetary value; they maximise expected UTILITY. Von Neumann and Morgenstern formalised this with an expected utility function, building on Bernoulli's insight that money carries diminishing marginal utility. Whether a consumer prefers a certain sum over an actuarially fair gamble of equal expected value depends on the curvature of their utility-of-wealth function.

Risk-averse — concave utility-of-wealth function; expected utility of a fair gamble is strictly less than the utility of its expected (certain) value, so the agent pays a premium to avoid risk (most economic agents are modelled this way).
Risk-neutral — linear utility-of-wealth function; the agent is indifferent between a certain sum and a fair gamble of equal expected value, and maximises expected monetary value directly.
Risk-loving — convex utility-of-wealth function; the agent strictly prefers the fair gamble to its certain expected value (the basis of lottery/gambling behaviour).

🧠 Certainty equivalent, risk premium and the Arrow-Pratt measure

The certainty equivalent (CE) of a gamble is the certain sum whose utility equals the gamble's expected utility: U(CE) = E[U(w)]. The risk premium is the gap RP = E(w) − CE — how much expected wealth a risk-averse agent would sacrifice to eliminate the risk entirely. NET has tested the formula for the Arrow-Pratt coefficient of absolute risk aversion directly: A(w) = −U″(w)/U′(w), a normalised measure of the utility function's concavity that is invariant to positive linear transformations of utility.

Key takeaways

Ordinal utility (indifference curves, MRS = Px/Py at equilibrium) replaced cardinal utility (MUx/Px = MUy/Py); non-intersecting, convex, negatively-sloped indifference curves are the well-behaved shape NET tests.
The Slutsky/Hicks decomposition splits a price change into a substitution effect (always negative) and an income effect (sign depends on normal/inferior); a Giffen good's dominant negative income effect produces an upward-sloping demand curve.
Revealed preference (WARP/SARP) derives consistent consumer behaviour from observed choices without assuming a utility function exists at all.
Returns to scale (long run, all factors variable) and the law of diminishing marginal returns (short run, one factor fixed) are distinct; MC cuts AVC and AC at their minimum points, and LAC is the envelope of SAC curves.
Expected utility (not expected monetary value) drives choice under uncertainty; concave/linear/convex utility-of-wealth functions define risk-averse/neutral/loving agents, with the Arrow-Pratt coefficient A(w) = −U″(w)/U′(w) measuring absolute risk aversion.

Practice questions (9)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

A convex indifference curve exhibits a diminishing marginal rate of substitution. This is best described as:
1. A falling ratio of two marginal utilities along a curve of constant satisfaction
2. A falling marginal utility of each good individually
3. A falling total utility as consumption rises
4. A rising price ratio between the two goods
Show answer
Answer: A — A falling ratio of two marginal utilities along a curve of constant satisfaction
Diminishing MRS is a statement about the changing ratio of marginal utilities along a fixed indifference curve, not about either good's own marginal utility falling — ordinal theory needs no assumption of diminishing marginal utility to derive it.
The Slutsky and Hicks decompositions of a price change differ chiefly in:
1. What is held constant while isolating the substitution effect — purchasing power (Slutsky) versus utility level (Hicks)
2. Whether the substitution effect can be positive
3. Whether the good is normal or inferior
4. Whether income is held constant in money terms
Show answer
Answer: A — What is held constant while isolating the substitution effect — purchasing power (Slutsky) versus utility level (Hicks)
Slutsky compensation restores just enough income to afford the original bundle at new prices (holds purchasing power); Hicks compensation restores just enough income to reach the original utility level (holds satisfaction) — both give a substitution effect that is always negative.
A Giffen good's demand curve slopes upward because:
1. Its negative income effect (it is inferior) outweighs the always-negative substitution effect
2. Its substitution effect is positive
3. Consumers have imperfect information about its price
4. It is a luxury good with high income elasticity
Show answer
Answer: A — Its negative income effect (it is inferior) outweighs the always-negative substitution effect
The substitution effect is always negative in sign (theory never allows it to reverse); a Giffen good is defined by a negative income effect large enough to dominate it, giving a net positive relationship between price and quantity demanded.
The Weak Axiom of Revealed Preference (WARP) requires that:
1. If bundle A is chosen when B was also affordable, B must never be chosen over A when A is affordable
2. Every consumer must have a differentiable utility function
3. Indifference curves must be linear
4. The consumer's income must remain constant across all price changes
Show answer
Answer: A — If bundle A is chosen when B was also affordable, B must never be chosen over A when A is affordable
WARP is a consistency requirement on observed choices alone, with no reference to a utility function; violating it means the consumer's choices contradict each other across two budget situations.
In the short run, the marginal cost curve intersects the average variable cost and average cost curves:
1. At their respective minimum points
2. At their respective maximum points
3. Only where output is zero
4. It never intersects them
Show answer
Answer: A — At their respective minimum points
This follows from the mathematical relationship between marginal and average curves: MC pulls AVC/AC down while MC is below them and pulls them up once MC rises above them, so MC must cross each exactly at its minimum.
Returns to scale and the law of diminishing marginal returns differ chiefly because:
1. Returns to scale applies when all inputs vary together (long run); diminishing returns applies when only one input varies with others fixed (short run)
2. Returns to scale is a short-run concept and diminishing returns a long-run one
3. They are two names for the identical relationship
4. Returns to scale applies only to labour
Show answer
Answer: A — Returns to scale applies when all inputs vary together (long run); diminishing returns applies when only one input varies with others fixed (short run)
Returns to scale is a long-run, all-factors-variable concept; the law of diminishing marginal returns describes the short run with at least one fixed factor — conflating the two is the commonest error NET tests here.
A risk-averse agent's utility-of-wealth function is:
1. Concave, so the expected utility of a fair gamble is less than the utility of its expected value
2. Convex, so the agent prefers the gamble to its expected value
3. Linear, so the agent is indifferent between the gamble and its expected value
4. Undefined at any wealth level below the mean
Show answer
Answer: A — Concave, so the expected utility of a fair gamble is less than the utility of its expected value
Concavity of the utility function is precisely what makes E[U(w)] < U(E(w)) — Jensen's inequality applied to a concave function — which is the mathematical definition of risk aversion.
Which of the following are properties of a well-behaved (standard) indifference curve?
1. It is negatively sloped
2. It is convex to the origin
3. A curve farther from the origin represents higher satisfaction
4. Two indifference curves for the same consumer can intersect
Show answer
Answer: A — It is negatively sloped; B — It is convex to the origin; C — A curve farther from the origin represents higher satisfaction
The first three are standard properties; the fourth is false — two indifference curves of the same consumer can never intersect, since that would require the consumer to rank the same pair of bundles inconsistently, violating transitivity of preference.
Name the coefficient, defined as A(w) = −U″(w)/U′(w), that measures an agent's degree of absolute risk aversion.
Numerical answer — type the value.
Show answer
Answer: Arrow-Pratt coefficient
The Arrow-Pratt coefficient of absolute risk aversion normalises the curvature of the utility-of-wealth function by its slope, giving a measure that is invariant to positive linear (affine) rescalings of utility — a common NET numerical/formula item.