3. (15) Suppose that there are two goods, housing and food. An individual has income I and faces prices for
housing and food of Ph and Pf , respectively. His or her demands for housing and food are given by:
q food = (1-a)C + (aI/Pf) + aB(Ph/Pf)
q housing = -aB + ((1-a)I/Ph) - (1-a)C(Pf/Ph)
where 0 0, B > 0, and suppose that each good is being consumed.
a. (5) Suppose that B > 0, and C > 0, but not too big. As income rises, what is the value of the
income elasticities of these two goods moving towards? Can you say which income elasticity is bigger than
1 for small values of I? (Hint, compare these demands with those when B = C = 0.)
b. (5) Suppose that B > 0, and C > 0, but not too big. As income rises, what is the value of the own
price elasticity for each of these goods moving towards? (Hint, compare these demands with those when B =
C = 0.)
c. (5) Since one of the goods has an income elasticity less than 1 and the other good has an income
elasticity greater than 1 one good is inferior and the other is a luxury. Consider two economies, each with the
same number of households and the same total income. In one economy all households have the same income.
In the other economy the rich have much more income than the poor. In fact assume that the poor have so little
income that their consumption of housing is practically 0. Which economy consumes more housing?
If you can understand that notation, then bravo to you, but I'll clean it up a bit after I get back from class.