David K.H. Begg, Gianluigi Vernasca-Economics-McGraw Hill Higher Education (2011)

CHAPTER 5 Consumer choice and demand decisions
Perfect substitutes
Perfect complements
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Figure S.19
Indifference curves for perfect substitutes and complements
whose relative price has fallen. Abstracting from income effects, goods are necessarily substitutes for one
another in a two-good world.
With more than two goods, some goods may be consumed jointly - pipes and pipe tobacco, bread and
cheese, electric cookers and electricity. These goods are complements.
Even with many goods, there is always a substitution effect away from goods whose relative price has risen.
However, substitution may not be towards all other goods. Consumers substitute away from goods
consumed jointly with the good whose price has risen.
Suppose the price of pipes rises. What will happen to the demand for pipe tobacco? (Ignore the income
effect, since expenditure on pipes is a tiny fraction of household budgets, so real incomes are only slightly
reduced.) Since pipes and pipe tobacco are used jointly, we expect the demand for pipe tobacco to fall
along with the number of pipes demanded. The demand curve for pipe tobacco shifts to the left in response
to the increase in pipe prices. Notice that this implies that the cross-price elasticity between those two
goods should be negative.
When goods are complements, a rise in the price of one good will reduce the demand for the complement,
both through the substitution effect (substituting away from the higher-priced activity) and, of course,
through the income effect (provided goods are normal).
Special cases are goods that are perfect substitutes or perfect complements. Perfect substitutes are goods that
are viewed as equal by consumers. In that case, the consumer always consumes the cheap one. Suppose
that, for you, Coca-Cola and Pepsi are exactly the same thing. Then you will drink the one that costs less.
On the other hand, perfect complements are goods that are always consumed together in fixed proportion,
for example one right shoe and one left shoe.
The indifference curves in these two particular cases are displayed in Figure 5.19.
Higher indifference curves imply higher utility. In the case of perfect substitutes, the indifference curves
are downward-sloping straight lines. Therefore, for perfect substitutes the marginal rate of substitution is
constant. In this particular case, at the optimal choice it is not true that the marginal rate of substitution is
equal to the slope of the indifference curve. We have a corner solution. Our consumer consumes only the
cheapest good.
The case of perfect complements is one where the property that consumers prefer 'more to less' does not
hold. Suppose you really like to eat your chocolate cake with a ball of vanilla ice cream on top. You prefer
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