ECC1000 Chap.5 Price Changes, Income Effects and the Work-Leisure Choice
Price Changes, Income Effects and the Work-Leisure Choice
One price change, two consequences
When a price moves, the budget line turns and its reach changes. The turn alters the rate at which one good exchanges for the other; the change in reach alters what the same money income commands. The unit separates the resulting change in the chosen bundle into a substitution effect and an income effect.
Neither is observable on its own, since only the move from one chosen bundle to another can be seen, so the decomposition is a construction rather than a measurement and the order it is done in is part of the answer.
The procedure, in the order that is marked
Draw the new budget line first, moving only the intercept belonging to the price that changed.
Then draw a compensated line parallel to the new one, shifted outward until it just touches the original indifference curve; its tangency is the intermediate bundle. The move from the original bundle to that intermediate bundle is the substitution effect, at constant utility and a new relative price.
The move from the intermediate bundle to the final one is the income effect, at constant relative price and reduced purchasing power.
The compensated line is a device rather than a real budget: nobody receives the compensation, and an answer that treats it as an actual transfer has changed the question.
One effect has a guaranteed sign, and one does not
The substitution effect always moves consumption away from the good that became relatively dearer, because the compensated line is constructed with the new slope while utility is held fixed.
The income effect has no guaranteed direction: for a normal good, reduced purchasing power lowers consumption, while for an inferior good it raises it. The total is therefore signed only once the type of good is known, and where the two effects oppose each other the total depends on which is larger.
Marks are lost by describing a movement without naming the mechanism, so each sentence should carry the bundle moved from and to, the line the move happened along, and the effect responsible.
A common phrasing error worth removing early
The income effect is not caused by a fall in income. The money income has not moved at all; it simply commands a smaller set of bundles than before.
Writing that income fell is a factual error about the diagram, and it is the most frequently repeated one in this topic. Write instead that the same income now reaches fewer bundles, which is both accurate and the phrasing the effect is named for.
The same model on a clock
The final Week 3 model puts consumer choice on a time budget.
A day holds a fixed number of hours split between free time and work, work converts hours into wages, and wages convert into consumption. Rearranged, the constraint is an ordinary budget line in which free time is a good whose price is the wage, so the wage is the slope and therefore the marginal rate of transformation. A wage rise pivots the line about the free-time intercept, which cannot move because a day is still a day.
It raises the price of free time, so the substitution effect pushes toward more work, while raising purchasing power, so for a normal good the income effect pushes the other way. Theory alone does not sign the net change in hours worked, and the honest answer names both effects and says which would have to dominate.
What this chapter covers
- 01
Why one price change produces two effects
- 02
Drawing the new line and the compensated line
- 03
The substitution effect and its guaranteed direction
- 04
The income effect, normal goods and inferior goods
- 05
Signing the total, and when it cannot be signed
- 06
Real purchasing power against money income
- 07
The time budget and the wage as its slope
- 08
What a wage rise does to hours worked
Two effects pulling against each other
- 1State what happens to the budget line and which intercept moves.
- 1Give the substitution effect and justify its direction.
- 1Give the income effect and justify its direction for this type of good.
- 1Say what determines the sign of the total.
Key terms
- Substitution effect
- The change in consumption caused by a change in relative prices with utility held constant.
- Income effect
- The change in consumption caused by a change in real purchasing power with relative prices held constant.
- Compensated line
- A constructed budget line at the new slope, shifted to touch the original indifference curve.
- Normal good
- A good whose consumption rises when real purchasing power rises.
- Inferior good
- A good whose consumption falls when real purchasing power rises.
- Time endowment
- The fixed number of hours available to be split between work and free time.
Price Changes, Income Effects and the Work-Leisure Choice FAQ
Why must the substitution effect be drawn before the income effect?
Because the intermediate bundle is defined by holding utility at its original level while applying the new relative price. Reversing the order defines a different intermediate bundle and produces different magnitudes for both effects, so the decomposition is only reproducible if the sequence is fixed.
Is the compensated line something the consumer actually receives?
No. It is a construction used to hold satisfaction still while the relative price changes, so that the two consequences of a price move can be separated. Nobody is paid the compensation, and treating it as a real transfer changes both the diagram and the question being answered.
Why is the total effect sometimes impossible to sign?
When the good is inferior, the two effects push in opposite directions, so the sign of the sum depends on which is larger. That is a statement about magnitudes rather than about direction, and the model supplies directions without supplying magnitudes, so extra information is needed before the total can be reported.
Why can the free-time intercept never move in the work-leisure diagram?
Because it represents doing no paid work at all, and the number of hours in a day is fixed regardless of the wage. Only the consumption intercept responds to the wage, which is why a wage change pivots the line about the free-time end rather than shifting it.
Does a higher wage always mean more hours worked?
Not necessarily. A higher wage raises the price of free time, which pushes toward more work through the substitution effect, and simultaneously raises purchasing power, which for a normal good pushes toward more free time. The net direction depends on which effect dominates, so an answer asserting more hours without that qualification overstates what the model delivers.
Exam move
Practise the construction on paper until the order is automatic: new line, compensated line, intermediate bundle, then final bundle. Annotate each arrow with the effect that produced it before writing any prose. When revising, take one scenario and run it twice, once treating the good as normal and once as inferior, so the difference in the conclusion becomes memorable rather than memorised.
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