Causes of a shift in the budget line

Causes of a Shift in the Budget Line (Cambridge A‑Level Economics 9708 – Topic 7.2)

Learning Objectives

• Recall the budget‑line equation and its graphical properties (intercepts, slope).
• List **all** factors that can move the budget line, including taxes, subsidies, ad‑valorem taxes and price controls.
• Explain how each factor changes the intercepts, the slope (opportunity cost) and the shape of the line.
• Distinguish the **substitution effect** from the **income effect** for any price‑change.
• Identify the welfare implications (consumer surplus, dead‑weight loss, fiscal cost).
• Apply the concepts to real‑world examples and exam‑style questions.

1. The Budget Line – Quick Recap

The budget line shows every affordable combination of two goods (Good X and Good Y) for a consumer with income \(I\) and prices \(p_X, p_Y\).

Equation

\[ p_X X + p_Y Y = I \]

• \(p_X\) – price of Good X
• \(p_Y\) – price of Good Y
• \(X,\,Y\) – quantities of the two goods
• \(I\) – consumer’s income (total expenditure budget)

Key graphical features

• X‑intercept: \(X = \dfrac{I}{p_X}\) (when \(Y=0\))
• Y‑intercept: \(Y = \dfrac{I}{p_Y}\) (when \(X=0\))
• Slope (opportunity cost of X in terms of Y): \(-\dfrac{p_X}{p_Y}\)

2. How the Budget Line Can Move

A shift occurs when the set of affordable bundles changes. Two geometric patterns are possible:

• Parallel (outward or inward) shift – both intercepts move, slope unchanged. Caused only by a change in income.
• Rotational (pivot) shift – one intercept stays fixed while the other moves, altering the slope. Caused by any change in relative prices (including taxes, subsidies, price controls, real‑wage changes).

2.1 Sketch Guidance (exam tip)

Draw a single diagram that contains:

• The original budget line (labelled “Original”).
• A parallel outward shift (labelled “Income ↑”).
• A pivot outward about the Y‑intercept (labelled “\(p_X\) ↓”).
• A pivot inward about the X‑intercept (labelled “\(p_Y\) ↑”).

Use different colours or line styles and clearly mark the intercepts and slopes. (Insert a hand‑drawn sketch or a diagram such as budget_line_shifts.png in the exam answer.)

2.2 Summary Table of All Causes

Cause	Effect on Intercepts	Direction of Shift	New Slope (opportunity cost)	Substitution vs. Income Effect	Typical Welfare Implication	Concrete Real‑World Example (2023‑24)
Increase in income (\(I\uparrow\))	Both X‑ and Y‑intercepts rise proportionally: \(X=\frac{I'}{p_X},\;Y=\frac{I'}{p_Y}\)	Parallel outward	\(-\dfrac{p_X}{p_Y}\) (unchanged)	Pure **income effect** – consumer can afford more of both goods.	Consumer surplus rises; no substitution effect.	UK household cash‑grant programme 2023 increased disposable income.
Decrease in income (\(I\downarrow\))	Both intercepts fall proportionally.	Parallel inward	\(-\dfrac{p_X}{p_Y}\) (unchanged)	Pure **income effect** – less can be bought of both goods.	Consumer surplus falls.	Post‑pandemic cost‑of‑living squeeze reduced real incomes.
Decrease in price of Good X (\(p_X\downarrow\))	X‑intercept rises to \(\frac{I}{p_X'}\); Y‑intercept unchanged.	Pivot outward about Y‑intercept	\(-\dfrac{p_X'}{p_Y}\) (flatter, \(|slope|\) ↓)	Substitution **away** from Y (X cheaper) + positive income effect.	Consumer surplus ↑; magnitude depends on elasticities.	UK 2023 reduction in VAT on books lowered \(p_X\) for “Good X = books”.
Increase in price of Good X (\(p_X\uparrow\))	X‑intercept falls; Y‑intercept unchanged.	Pivot inward about Y‑intercept	\(-\dfrac{p_X'}{p_Y}\) (steeper, \(|slope|\) ↑)	Negative substitution (X less attractive) + negative income effect.	Consumer surplus ↓; possible dead‑weight loss if market is competitive.	UK 2023 increase in fuel duty raised the price of gasoline (Good X).
Decrease in price of Good Y (\(p_Y\downarrow\))	Y‑intercept rises; X‑intercept unchanged.	Pivot outward about X‑intercept	\(-\dfrac{p_X}{p_Y'}\) (flatter)	Substitution toward Y + positive income effect.	Consumer surplus ↑.	UK 2023 supermarket price war on fresh fruit lowered \(p_Y\).
Increase in price of Good Y (\(p_Y\uparrow\))	Y‑intercept falls; X‑intercept unchanged.	Pivot inward about X‑intercept	\(-\dfrac{p_X}{p_Y'}\) (steeper)	Negative substitution (Y less attractive) + negative income effect.	Consumer surplus ↓.	UK 2023 increase in council tax rates (treated as price of “leisure” good).
Specific (per‑unit) tax on Good X	Effective price becomes \(p_X^{new}=p_X+t\); same pattern as \(p_X\uparrow\).	Pivot inward about Y‑intercept	\(-\dfrac{p_X+t}{p_Y}\)	Substitution away from X + negative income effect.	Dead‑weight loss: \(\Delta DWL\approx\frac{1}{2}\times t \times \Delta Q\).	UK “sugar‑tax” on soft drinks (per‑litre levy) raises the price of sugary drinks.
Ad‑valorem tax on Good Y (percentage of price)	Effective price \(p_Y^{new}=p_Y(1+\tau)\); same pattern as \(p_Y\uparrow\).	Pivot inward about X‑intercept	\(-\dfrac{p_X}{p_Y(1+\tau)}\)	Substitution away from Y + negative income effect.	Dead‑weight loss calculated as \(\frac{1}{2}\times \tau p_Y \times \Delta Q\).	UK 2023 increase in VAT on luxury cars (ad‑valorem tax).
Subsidy on Good Y (per‑unit)	Effective price \(p_Y^{new}=p_Y-s\); same pattern as \(p_Y\downarrow\).	Pivot outward about X‑intercept	\(-\dfrac{p_X}{p_Y-s}\)	Substitution toward Y + positive income effect.	Potential welfare gain if subsidy corrects a market failure; otherwise fiscal cost.	UK 2023 Renewable Heat Incentive (subsidy on biomass heating – Good Y).
Price ceiling on Good X (binding)	Effective price forced down to \(p_X^{cap}	Pivot outward about Y‑intercept (but may create excess demand).	\(-\dfrac{p_X^{cap}}{p_Y}\)	Substitution toward X + positive income effect; possible shortage.	Consumer surplus rises for those who obtain X; dead‑weight loss from rationing.	UK 2023 rent‑control limits on private rentals (Good X = housing).
Price floor on Good Y (binding)	Effective price forced up to \(p_Y^{floor}>p_Y\); same geometry as \(p_Y\uparrow\).	Pivot inward about X‑intercept (may create surplus).	\(-\dfrac{p_X}{p_Y^{floor}}\)	Substitution away from Y + negative income effect; possible surplus.	Consumer surplus falls; dead‑weight loss from unsold surplus.	UK 2023 minimum support price for wheat (Good Y = agricultural output).
Change in real wage (labour‑leisure choice)	In leisure‑consumption diagram: intercept for consumption rises to \(wT\); intercept for leisure falls to 0 (leisure measured in hours).	Pivot outward for consumption, inward for leisure (steeper slope \(-w\)).	Slope becomes \(-w\) (steeper when \(w\uparrow\)).	Strong substitution away from leisure; income effect depends on whether the consumer is a net labour supplier.	Welfare impact hinges on the balance of the two effects; can raise overall utility if labour is valued more highly.	UK 2023 increase in the National Minimum Wage → higher real wage.

3. Concise Reminder – Substitution vs. Income Effects

When a price changes:

• Substitution effect: always works **opposite** to the price change – a cheaper good is consumed more, an expensive good is consumed less.
• Income effect: depends on whether the good is normal (consumption rises with higher real income) or inferior (consumption falls). For most A‑Level questions assume the good is normal unless stated otherwise.

4. Quick Welfare‑Estimation Tools (AO2/AO3)

• Change in Consumer Surplus (ΔCS) (for a small linear price change):
  \[ \Delta CS \approx \tfrac{1}{2}\,\Delta P \times \Delta Q \] where \(\Delta P\) is the price change and \(\Delta Q\) the resulting change in quantity demanded.
• Dead‑Weight Loss (DWL) from a tax or price control:
  \[ \text{DWL} \approx \tfrac{1}{2}\times (\text{tax or price gap})\times (\text{reduction in quantity}) \]
• These approximations are acceptable in exam calculations when the demand curve is assumed linear.

5. Detailed Explanations of Each Cause

5.1 Change in Income (or Total Expenditure Budget)

• New equation: \(p_X X + p_Y Y = I'\).
• Both intercepts shift outward (or inward) by the same proportion; slope unchanged.
• Only a **pure income effect** – no change in relative prices.

5.2 Change in the Price of Good X (\(p_X\))

• New equation: \(p_X' X + p_Y Y = I\).
• If \(p_X'\!<\!p_X\): X‑intercept rises, Y‑intercept unchanged, slope becomes \(-p_X'/p_Y\) (flatter).
• If \(p_X'\!>\!p_X\): opposite – pivot inward, steeper slope.
• Both substitution (relative‑price) and income (real‑purchasing‑power) effects operate.

5.3 Change in the Price of Good Y (\(p_Y\))

• Analogous to 5.2, but the rotation is about the X‑intercept.
• Price fall → pivot outward, flatter slope \(-p_X/p_Y'\); price rise → pivot inward, steeper slope.

5.4 Taxes, Subsidies and Price Controls

• Specific (per‑unit) tax: effective price \(p_X^{new}=p_X+t\). Treat as a price increase.
• Ad‑valorem tax: effective price \(p_Y^{new}=p_Y(1+\tau)\). Treat as a price increase.
• Subsidy (per‑unit): effective price \(p_Y^{new}=p_Y-s\). Treat as a price decrease.
• Price ceiling (binding): forces price down to \(p_X^{cap}\); same geometry as a price fall but may create excess demand.
• Price floor (binding): forces price up to \(p_Y^{floor}\); same geometry as a price rise but may create surplus.
• All generate substitution and income effects and produce welfare changes (consumer surplus, DWL, fiscal cost).

5.5 Real‑Wage Changes – Labour‑Leisure Decision

• Budget constraint in leisure‑consumption diagram: \(wL + C = wT\) (where \(L\) = leisure hours, \(C\) = consumption, \(T\) = total time).
• Higher real wage \(w\) raises the slope \(-w\) (steeper), rotating the line inward for leisure and outward for consumption.
• Strong substitution away from leisure; income effect depends on whether the individual is a net supplier of labour.

6. Linking to Core Cambridge Concepts

• Scarcity & Choice: The budget line visualises the trade‑off imposed by limited resources.
• Opportunity Cost (Margin): The slope \(-p_X/p_Y\) is the marginal rate of transformation between the two goods.
• Efficiency: Any point on the line uses the entire budget (technical efficiency).
• Government Role: Taxes, subsidies and price controls illustrate how policy can alter consumer choices and welfare.
• Progress & Development: Real‑wage movements reflect labour‑market developments that affect household welfare.

7. Worked Example (Full Calculation & Diagram Guidance)

Initial data

• Income \(I = £120\)
• Price of Good X: \(p_X = £4\)
• Price of Good Y: \(p_Y = £6\)

Budget equation: \(4X + 6Y = 120\)

Intercepts

• X‑intercept: \(120/4 = 30\) units
• Y‑intercept: \(120/6 = 20\) units

Scenario A – Income rises to £150

• New line: \(4X + 6Y = 150\)
• New intercepts: X = 37.5, Y = 25
• Shift: parallel outward; slope stays \(-4/6\).

Scenario B – Price of Good X falls to £3 (income unchanged)

• New line: \(3X + 6Y = 120\)
• New X‑intercept: \(120/3 = 40\); Y‑intercept remains 20.
• Shift: pivot outward about Y‑intercept; new slope \(-3/6 = -0.5\) (flatter).
• Effects:
  • Substitution: X becomes cheaper relative to Y → move toward X.
  • Income: Real purchasing power rises → can afford more of both goods.

Diagram suggestion

• Draw the original line (black), the parallel outward line (blue) and the pivoted line (red).
• Label intercepts, slopes and the type of shift.
• Indicate the substitution and income effects with arrows.

8. Typical Exam Question Formats

1. Diagram‑only: “Draw and label the effect on the budget line of a 20 % fall in the price of Good X, holding income constant.”
2. Calculation + diagram: Provide income and prices, ask for new intercepts and to illustrate the shift.
3. Analysis: “Explain how a specific tax on Good Y affects the consumer’s choice and welfare. Include substitution and income effects.”
4. Evaluation: “Assess whether a subsidy on Good X is an efficient way of increasing consumption of X. Use the budget‑line framework in your answer.”

9. Key Take‑aways

• Income changes → parallel shift; slope unchanged.
• Price changes (including taxes, subsidies, price controls, real‑wage) → pivot; slope changes to \(-p_X'/p_Y\) or \(-p_X/p_Y'\).
• Every price change generates a **substitution effect** (always opposite to the price movement) and an **income effect** (positive if the good is normal and the price falls, negative if the price rises).
• Welfare can be measured via changes in consumer surplus (≈½ ΔP·ΔQ) and dead‑weight loss (≈½ tax × quantity loss).