Suppose A and B have the following inverse demand curves for

Suppose A and B have the following (inverse) demand curves for fruity pebbles: P = 150 – 3QA P = 150 – 1.5QB. If they are the only two people in the fruity pebbles market, then the market demand is:

A. P = 150 – Q

B. P = 300 – 4.5 Q

C. Q = 66.67 – 2/9 P

D. Q = 60 – P

E. P = 100 – 6Q

Solution

For A,

P = 150 - 3QA

QA = (150 - P) / 3 = 50 - 0.33P

For B,

P = 150 - 1.5QB

QB = (150 - P) / 1.5 = 100 - 0.67P

Market demand is the horizontal summation of QA and QB:

Q = QA + QB

Q = 50 - 0.33P + 100 - 0.67P

Q = 150 - P

P = 150 - Q

Correct option (A).