The following is intended to explore what kinds of own-price demand relationships are
logically possible in a two-good model with exogenous income (unless otherwise specified).
For each of the following, indicate whether the relationship is possible or not and explain:
(a) Tastes are homothetic and the own-price demand relationship is positive.
Answer: This is not possible. When tastes are homothetic, all goods are normal goods. Price
in creases for normal goods result in a negative substitution effect and a negative income
effect in the same direction. Thus, the own-price demand relationship must be negative.
(b) A good is inferior and its own-price relationship is negative.
Answer: This is possible. When a good is inferior, then an increase in the price results in a
negative substitution effect and a positive income effect. If the income effect is smaller than
the substitution effect, the good is “regular inferior” — and the own-price demand curve is
downward sloping (i.e. the own-price demand relationship is negative). (If the income effect
is larger than the substitution effect, the own-price demand curve slopes up and the good is a
Giffen good.)
(c) In a model with endogenous income, a good is normal and its own-price demand
relationship is negative.
Answer: Yes, this is possible. Consider the case where all income is endogenously derived
from owning a quantity E of x1. This is illustrated in panel (a) of Graph 9.1 where the
shallower budget corresponds to a lower price for good x1 and the steeper budget to a higher
price for x1. In panel (b), the substitution effect from A to B is illustrated — clearly
suggesting that, as p1 increases, consumption of x1 declines. If x1 is a normal good (as
logically possible in a two-good model with exogenous income (unless otherwise specified).
For each of the following, indicate whether the relationship is possible or not and explain:
(a) Tastes are homothetic and the own-price demand relationship is positive.
Answer: This is not possible. When tastes are homothetic, all goods are normal goods. Price
in creases for normal goods result in a negative substitution effect and a negative income
effect in the same direction. Thus, the own-price demand relationship must be negative.
(b) A good is inferior and its own-price relationship is negative.
Answer: This is possible. When a good is inferior, then an increase in the price results in a
negative substitution effect and a positive income effect. If the income effect is smaller than
the substitution effect, the good is “regular inferior” — and the own-price demand curve is
downward sloping (i.e. the own-price demand relationship is negative). (If the income effect
is larger than the substitution effect, the own-price demand curve slopes up and the good is a
Giffen good.)
(c) In a model with endogenous income, a good is normal and its own-price demand
relationship is negative.
Answer: Yes, this is possible. Consider the case where all income is endogenously derived
from owning a quantity E of x1. This is illustrated in panel (a) of Graph 9.1 where the
shallower budget corresponds to a lower price for good x1 and the steeper budget to a higher
price for x1. In panel (b), the substitution effect from A to B is illustrated — clearly
suggesting that, as p1 increases, consumption of x1 declines. If x1 is a normal good (as
