Indifference curves, the budget line and consumer equilibrium
An indifference curve joins bundles giving equal satisfaction. The best affordable bundle is where it touches the budget line, so MRS = Px/Py.
The ordinal approach
Hicks and Allen showed that we do not need to measure utility; the consumer only needs to rank bundles. An indifference curve (IC) joins all combinations of two goods that give the consumer the same satisfaction. A set of ICs is an indifference map: curves further from the origin give higher satisfaction. The slope of an IC is the marginal rate of substitution (MRSxy): the amount of Y the consumer is willing to give up for one more unit of X while staying equally well off. MRS diminishes as the consumer gets more X, because each extra X is worth less to them.
An indifference schedule with diminishing MRS
| Bundle | Good X | Good Y | MRSxy (Y given up for 1 X) |
|---|---|---|---|
| A | 1 | 18 | - |
| B | 2 | 13 | 18 − 13 = 5 |
| C | 3 | 9 | 13 − 9 = 4 |
| D | 4 | 6 | 9 − 6 = 3 |
| E | 5 | 4 | 6 − 4 = 2 |
Properties of indifference curves
- They slope downwards from left to right: to get more X, the consumer must give up some Y to stay equally satisfied.
- They are convex to the origin, because MRS diminishes.
- Two indifference curves never intersect; if they did, one bundle would give two different levels of satisfaction.
- A higher indifference curve shows a higher level of satisfaction (more of at least one good).
- They need not be parallel to each other.
- They normally do not touch either axis, since the consumer wants some of both goods.
Worked example 1: the budget line and its shifts
A consumer has Rs. 2,000. Good X costs Rs. 100 and good Y costs Rs. 50. Find the budget line, its intercepts and slope. What happens if (a) income rises to Rs. 3,000, (b) Px falls to Rs. 50?
- Budget line: 100X + 50Y = 2,000.
- Maximum X (Y = 0) = 2,000 ÷ 100 = 20. Maximum Y (X = 0) = 2,000 ÷ 50 = 40.
- Slope = −Px ÷ Py = −100 ÷ 50 = −2: one more X costs 2 units of Y.
- (a) Income Rs. 3,000: max X = 3,000 ÷ 100 = 30, max Y = 3,000 ÷ 50 = 60. Slope still −2, so the line shifts out parallel.
- (b) Px = Rs. 50: max X = 2,000 ÷ 50 = 40, max Y still 40. The line pivots outward on the X axis; slope becomes −1.
Original line from (20, 0) to (0, 40), slope −2. Higher income shifts it out parallel; a fall in Px pivots it outward along the X axis.
Consumer equilibrium
The consumer reaches the highest indifference curve the budget allows. This is where an IC is tangent to the budget line. Two conditions hold: (1) MRSxy = Px ÷ Py, so the rate at which the consumer is willing to swap equals the rate at which the market lets them swap; (2) the IC is convex at that point. If MRSxy is greater than Px ÷ Py, the consumer values X more than the market charges for it, so they should buy more X. If MRSxy is smaller, they should buy less X.
Worked example 2: finding the equilibrium bundle
The consumer's preferences give MRSxy = Y ÷ X (as with the utility function U = XY). Income is Rs. 2,000, Px = Rs. 100, Py = Rs. 50. Find the equilibrium bundle. Is the bundle X = 5, Y = 30 a good choice?
- Equilibrium needs MRSxy = Px ÷ Py: Y ÷ X = 100 ÷ 50 = 2, so Y = 2X.
- Put Y = 2X into the budget: 100X + 50(2X) = 2,000 → 200X = 2,000 → X = 10.
- Y = 2 × 10 = 20. Check spending: 100 × 10 + 50 × 20 = 1,000 + 1,000 = Rs. 2,000. ✓
- Bundle (5, 30) costs 500 + 1,500 = Rs. 2,000, so it is on the budget line, but MRS = 30 ÷ 5 = 6, which is greater than 2.
- At (5, 30) the consumer values one X at 6 Y, while it costs only 2 Y, so they should buy more X and less Y.
Equilibrium: X = 10, Y = 20 (MRS = 2 = Px/Py). The bundle (5, 30) is affordable but not the best.
A family choosing between mobile data and TV packages on a fixed monthly budget is moving along a budget line. Firms like Dialog design bundles and price cuts that pivot the customer's budget line, to move them to a new best choice that includes more of the firm's product.
Short answer: “What is the marginal rate of substitution?” The amount of good Y a consumer is willing to give up to get one more unit of X while staying on the same indifference curve.
Structured question: “State four properties of indifference curves.” Downward sloping, convex to the origin, never intersect, higher curves mean higher satisfaction; explain each in one line.
Essay: “Explain consumer equilibrium using indifference curve analysis.” Define IC, MRS and the indifference map, list properties, derive the budget line, show tangency (MRS = Px/Py) with a diagram, and explain why other points are not optimal.
Tangency is the target: highest IC that just touches the budget line, where MRS = Px/Py. ICs are D-C-N-H: Downward, Convex, Never cross, Higher is better.