What is Budget Constraint?
The budget constraint represents all combinations of two goods a consumer can afford given their income and the prices of those goods. It's the boundary between affordable and unaffordable bundles. The constraint shifts with changes in income or prices.
Budget constraint is the equation P_X·Q_X + P_Y·Q_Y = M, where P_X and P_Y are prices, Q_X and Q_Y are quantities, and M is total income. All points on or inside the line are affordable.
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Step-by-step worked examples
Income = $100, price of X = $5, price of Y = $10. What is the maximum Y if you buy 8 units of X?
Spent on X = 5 × 8 = $40 Remaining for Y = 100 − 40 = $60 Max Y = 60 / 10 = 6 units
If you have $200, Px = $20, Py = $4, find the Y-intercept (max Y with zero X).
Budget equation: 20·Qx + 4·Qy = 200 When Qx = 0: 4·Qy = 200 Qy = 50 units
Income rises from $80 to $120. How does the X-intercept change if Px = $10?
Old X-intercept: 80/10 = 8 units New X-intercept: 120/10 = 12 units Intercept increases by 4 units (outward parallel shift).
Flashcards
Quick quiz
Q1.If M = $100, Px = $4, Py = $5, and you buy 10 X, how much Y can you afford?
Q2.When income increases, the budget line…
Q3.What is the slope of the budget line Px·Qx + Py·Qy = M?
Q4.If Px doubles but M and Py stay the same, the X-intercept…
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Common mistakes
The budget constraint is always upward-sloping. — Correct: It always slopes downward (−Px/Py) — you trade off one good for the other.
Points outside the budget line are affordable. — Correct: Only points on or inside the line are affordable; outside means spending exceeds income.
The budget line doesn't move if income changes. — Correct: Income change shifts the entire line outward (more income) or inward (less income).
The slope of the budget line equals the ratio of quantities. — Correct: The slope is −Px/Py, the price ratio — not quantity related.
FAQ
What is the budget constraint formula?
Px·Qx + Py·Qy = M — total spending on both goods equals your income.
What does the budget constraint tell us?
It defines all affordable combinations of goods. Optimal choice lies on the budget line where it's tangent to an indifference curve.
How does a price change affect the budget line?
If Px increases, the X-intercept decreases and the line rotates inward. The line's slope (−Px/Py) also steepens.
Why is the budget line straight, not curved?
Prices are fixed per unit, so the trade-off is linear. The budget constraint is always a straight line (unless income varies with quantity).