7.1 Imagine a market for X composed of four individuals: Mr. Pauper (P), Ms. Broke (B), Mr.

Average (A), and Ms. Rich (R). All four have the same demand function for X: It is a function of income (I ), PX, and the price of an important subtitute (Y ), for X:

X

a. What is the market demand function for X? If PX
PY
1, IP
IB
16, IA
25, and IR
100, what is the total market demand for X? What is eX,PX

? eX,PY

? eX,I?

b. If PX doubled, what would be the new level of X demanded? If Mr. Pauper lost his job and his income fell 50 percent, how would that affect the market demand for X? What if Ms. Rich’s income were to drop 50 percent? If the government imposed a 100 percent tax on Y, how would the demand for X be affected?

c. If IP
IB
IA
IR
25, what would be the total demand for X? How does that figure compare with your answer to (a)? Answer

(b) for these new income levels and PX  PY
1.

d. If Ms. Rich found Z a necessary complement to X, her demand function for X might be described by the function X
.

What is the new market demand function for X? If PX
PY
PZ
1 and income levels are those described by (a), what is the demand for X? What is eX,PX

? eX,PY

? eX,I? eX,PZ

? What is the new level of demand for X if the price of Z rises to 2? Notice that Ms. Rich is the only one whose demand for X drops.