Consumer’s budget and optimal choice

The essentials

A consumer with money income M faces prices p₁ and p₂ for two goods. A bundle (x₁, x₂) is affordable if p₁x₁ + p₂x₂ ≤ M. The set of all affordable bundles is the budget set. The bundles that cost exactly M lie on the budget line: p₁x₁ + p₂x₂ = M.

The budget line meets the x₁-axis at M ÷ p₁ and the x₂-axis at M ÷ p₂. Its slope is −p₁ ÷ p₂, showing how many units of good 2 must be given up to get one more unit of good 1 (the market rate of exchange).

Key points

• Income change: a rise in M with prices fixed shifts the budget line parallel outward; a fall shifts it inward.
• Price change: a fall in p₁ rotates the line outward around the x₂-intercept; the x₁-intercept moves out.
• Preferences: an indifference curve joins bundles that give the same satisfaction. With monotonic preferences, more of at least one good with no less of the other is preferred.
• Marginal rate of substitution (MRS): the amount of good 2 the consumer is willing to give up for one more unit of good 1; it equals the absolute slope of the indifference curve. MRS diminishes along the curve, which makes indifference curves convex to the origin.
• Higher indifference curves show higher satisfaction; two indifference curves never intersect.
• Optimum choice: the consumer chooses the bundle where the budget line is tangent to the highest attainable indifference curve, so MRS = p₁ ÷ p₂.

Exam tips

• For "maximum quantity" questions, divide income by the price of that good.
• To test whether a bundle is in the budget set, compute its cost and compare it with M.

Common mistakes

• Writing the slope as −p₂ ÷ p₁. With good 1 on the horizontal axis the slope is −p₁ ÷ p₂.
• Thinking a price change causes a parallel shift. Only an income change (or equal proportional change in both prices) does that.