CB2400 Chap.7 Budgets and Consumer Choice
Budgets and Consumer Choice
The budget line records affordability
Income and prices generate the constraint I = PxX + PyY. Each intercept shows the maximum quantity purchasable when all income is spent on one good, while the slope magnitude Px/Py gives the market trade-off. More income shifts the line outward in parallel.
A price change rotates it around the intercept of the good whose price did not change.
Interior choice needs two conditions
A smooth interior optimum lies on the budget line and reaches the highest attainable indifference curve. At that point MRSx = Px/Py, equivalently MUx/Px = MUy/Py.
The first equation fixes affordability; the second prevents a utility-improving reallocation of the last dollar between goods.
Corners and kinks require comparison
Perfect substitutes may place all spending on the good with higher marginal utility per dollar. Perfect complements normally choose the fixed-proportion kink.
Quantity discounts can create several budget segments, so a candidate must be checked against the range that generated it. The general rule survives every case: compare feasible candidates and select the bundle on the highest attainable indifference curve.
What this chapter covers
- 01
budget equation
- 02
intercepts and slope
- 03
income and price changes
- 04
interior tangency
- 05
corner solutions
- 06
kinked budget lines
Worked example · free
Solve an interior consumer optimum
- 2Write the budget equation and marginal utilities.
- 3Apply MRSx = Px/Py to obtain an input ratio.
- 4Substitute into the budget and verify both conditions.
Key terms
- Budget Constraint
- The boundary and set of bundles affordable at stated income and prices.
- Budget Intercept
- The maximum amount of one good affordable when no income buys the other.
- Interior Optimum
- A best affordable bundle with positive quantities of both goods and a tangency.
- Corner Solution
- An optimum at an endpoint where one good may be consumed in zero quantity.
- Substitution Effect
- The choice response to a relative-price change while utility is held constant.
Budgets and Consumer Choice FAQ
What moves when income rises?
With both prices unchanged, each intercept increases in the same proportion and the budget line shifts outward in parallel. Its slope remains minus Px divided by Py because the relative price has not changed. The chosen quantities then depend on whether each good is normal or inferior over the relevant range.
Why is tangency not always valid?
Tangency assumes a smooth interior contact. Straight indifference curves can select a corner, L-shaped curves select a kink, and a discount can kink the budget line itself. In those cases, identify all feasible candidates and compare utility instead of imposing equality between slopes where no interior tangency exists.
How should a kinked budget be solved?
Write the equation for each segment and its allowed quantity range. Find any optimum candidate within each segment, reject solutions outside their own ranges, and include the kink as a candidate. Evaluate affordability and utility at the surviving points before choosing the highest attainable ranking.
Exam move
Start every consumer-choice problem by drawing the intercepts and writing I = PxX + PyY. Next classify the preference shape. Use tangency only for a smooth interior case, marginal utility per dollar for substitute corners, and fixed proportions for complements. For discounts, attach a valid range to every segment and test the kink explicitly.
Compute both intercepts even when the question asks only for a bundle; they make an immediate feasibility check. An income change moves both intercepts proportionally and preserves slope, whereas one price change rotates the line around the other good's intercept. For an interior solution, keep the budget and MRS equations on separate lines, solve them jointly, and substitute the answer into both.
Expenditure must equal income under more-is-better preferences, and the MRS must equal the relative price. For perfect substitutes, compare marginal utility per dollar and choose the better endpoint unless the ratios tie. For perfect complements, impose the fixed consumption proportion before using the budget.
With a piecewise price, reject candidates that fall outside the segment whose equation produced them, include the kink, and compare utility across the survivors. Close every solution by naming the case: interior tangency, corner, complement kink or piecewise candidate comparison.
Redraw one solved problem after changing only income and another after changing only Px, then explain why the first is parallel and the second rotates.
Working through Budgets and Consumer Choice in CB2400? Sia is AskSia’s AI Economics tutor — ask any CB2400 Budgets and Consumer Choice question and get a clear, step-by-step explanation grounded in how CB2400 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.