Consumer choice theory explains how individuals allocate their limited income across competing wants. The framework is utility maximisation subject to a budget constraint — and the formal apparatus produces useful predictions about behaviour even when the consumer doesn't literally compute the math.
Utility and preferences
Utility is a representation of preferences. If a consumer prefers bundle A to bundle B, then U(A) > U(B). Utility is ordinal (we care about rankings, not the numerical values) and represents subjective valuation. Two key assumptions about preferences:
- Completeness — for any two bundles, the consumer can say which is preferred (or indifferent)
- Transitivity — if A ≻ B and B ≻ C, then A ≻ C
- More-is-better (monotonicity) — bigger bundles are preferred (for goods, as opposed to bads)
- Convexity — averages are preferred to extremes; a 50-50 mix of two indifferent bundles is at least as good as either
Indifference curves
An indifference curve shows all bundles giving the same utility. Higher curves represent higher utility. Indifference curves don't cross (transitivity); they slope downward (more-is-better); they're typically convex to the origin (convexity).
Marginal rate of substitution (MRS)
MRS_xy = − dy/dx along an indifference curve = MU_x / MU_y • MU_x = marginal utility of good x (the utility from one more unit of x) • MU_y = marginal utility of good y The MRS tells you how much of y the consumer is willing to give up for one more unit of x while remaining indifferent. As you consume more x and less y, MRS typically falls (the diminishing marginal rate of substitution) — reflecting that the more you have of something, the less you value the marginal unit relative to alternatives.
The budget constraint
Budget constraint
P_x · x + P_y · y ≤ M • P_x, P_y = prices of goods x and y • x, y = quantities consumed • M = consumer's income (or budget) The slope of the budget line is −P_x/P_y — the relative price of x in terms of y. Higher P_x makes the budget line steeper (more y given up per unit of x affordable). The intercepts: M/P_x on the x-axis (all income on x), M/P_y on the y-axis (all on y).
Optimal choice — the tangency condition
The consumer maximises utility by choosing the bundle on the budget line that touches the highest indifference curve. Geometrically, this is the point where the indifference curve is tangent to the budget line — equal slopes.
Optimal-choice condition
MU_x / MU_y = P_x / P_y or equivalently: MU_x / P_x = MU_y / P_y The second form: 'equate the marginal utility per shilling spent on each good'. In economic intuition: at the optimum, the next shilling of expenditure delivers the same marginal utility whether spent on x or y. If it didn't — say MU_x/P_x > MU_y/P_y — the consumer could rebalance toward more x and gain net utility.
Income effects
When income changes, the budget line shifts parallel (no change in relative prices). For normal goods, demand rises with income. For inferior goods, demand falls. Engel curves describe this:
- Normal goods — demand rises with income. Most goods. Income elasticity positive (e_M > 0)
- Luxury goods — demand rises more than proportionally with income. e_M > 1. Expensive cars, restaurant meals, foreign vacations
- Necessities — demand rises with income but less than proportionally. 0 < e_M < 1. Basic food, clothing
- Inferior goods — demand falls as income rises. e_M < 0. Ugali in some African contexts; second-hand clothing; rural-bus travel as income rises and matatu/car becomes accessible
Engel's law
Engel (1857): as income rises, the share of expenditure spent on food falls. Empirically robust across countries and centuries. Applied to Kenya household-expenditure data (KIHBS 2015/16): the poorest 20% of households spend ~62% of budget on food; the richest 20% spend ~28%. The implication: any policy that taxes food (broad-base VAT on food) is mildly REGRESSIVE in budget-share terms even though everyone faces the same VAT rate.
The Slutsky decomposition
When a price changes (say P_x rises), the consumer responds with a substitution effect (rebalance away from now-relatively-expensive x) AND an income effect (the price rise effectively makes you poorer in real terms, shifting demand for all goods).
Slutsky decomposition of the price effect
Total effect = Substitution effect + Income effect • Substitution effect — the change in demand for x if the consumer were compensated to remain on the original indifference curve. Always negative (higher P_x reduces consumption of x along the indifference curve) • Income effect — the change in demand from the loss of real purchasing power. Sign depends on whether x is normal (negative income effect; demand falls further) or inferior (positive income effect; partially offsets substitution effect) For most goods (normal goods), both effects work in the same direction → demand for x falls strongly when P_x rises. For inferior goods, the two effects work in opposite directions; the net effect is usually still downward but less strongly so. Giffen good: a theoretical inferior good for which the income effect dominates and demand RISES with price. Extremely rare; debate over whether genuine empirical examples exist.
Subsistence and low-income contexts
Standard consumer theory assumes consumers have flexibility — they can rebalance their bundle freely. Subsistence contexts (extreme poverty) violate this:
- Subsistence floor — some consumption levels (calories, basic housing) are non-negotiable. Below them, the consumer doesn't survive. The utility function effectively has a discontinuity (very low utility below subsistence)
- Risk and shock — poor consumers face frequent shocks (drought, illness, livestock loss). Static consumer theory assumes a smooth budget; reality is volatile
- Time and self-control — choices in poverty are often dominated by immediate constraints (today's food); standard theory assumes time-consistent utility maximisation. The Behavioural Economics course explores when this breaks down
- Information constraints — consumers may not know about all available alternatives or prices
- Social constraints — informal social-insurance obligations (family transfers, communal obligations) constrain individual choice in ways the textbook ignores
The income-vs-consumption smoothing gap
African households at the median income level face large variations between agricultural seasons and other shocks. Consumption smoothing — keeping consumption stable across income fluctuations — is what the textbook predicts via savings and borrowing. In practice, low-income households can't smooth perfectly because of credit constraints (can't borrow when poor) and savings constraints (can't save much when subsisting). Real consumption tracks income more closely than the theoretical optimum would predict. This is why income shocks have larger welfare effects on the poor than the rich.
Demand for differentiated goods
When goods are not perfect substitutes (consumers care about quality, brand, features), demand is structured by characteristics rather than just quantity. Examples in African markets:
- Mobile-money services — M-Pesa vs Airtel Money. Network effects mean consumers value the size of the user base, not just price
- Smartphone — feature combinations matter (camera, screen, battery), not just price
- Education — public vs private schools; cheap private vs expensive private. Quality differentiation
- Telecoms data plans — bundled vs unbundled; speed vs cost trade-offs
Exercise
A Kenyan low-income household earns KES 25,000/month and spends as follows: food 60%, housing 18%, transport 10%, schooling 7%, other 5%. Now suppose the price of food rises by 25%, with income unchanged. (1) Compute the new budget allocation if the household tries to maintain food quantity (no substitution). (2) Compute the income effect. (3) Apply the Slutsky decomposition: what will the household actually do? (4) What's the welfare impact, and what policy could buffer it?