Suppose that three consumers are in the market for good X. Consumer 1's (inverse) demand is P_X = 20 - Q_X; Consumer 2's (inverse) demand is P_X = 20 - 2Q_X; and Consumer 3's (inverse) demand is P_X = 20 - 4Q_X. When P_X = $10, the market will demand: A) 17.5 units and the inverse market demand curve is P_X = 20 - 0.5714Q_X. B) -30 units and the inverse market demand curve is P_X = 60 - 7Q_X. C) 17.5 units and the inverse market demand curve is P_X = 60 - 7Q_X. D) None of the statements is correct.

Question

Quizplus · Accepted Answer

To find the market demand, we simply add up the individual demands of each consumer at the given price of $10.
QD = QS1U1B1XS1U1B0 + QS2U1B1XS1U1B0 + QS3U1B1XS1U1B0
QD = (20 - 1*10)/(1) + (20 - 2*10)/(1) + (20 - 4*10)/(1)
QD = 17.5 units
To find the inverse market demand curve, we add up the individual inverse demand curves and solve for P in terms of Q.
P = 20 - Q/1 - Q/2 - Q/4
P = 60/7 - 7Q/28
P = $8.57 - 0.25Q
Therefore, the correct answer is A, which states that the market will demand 17.5 units and the inverse market demand curve is PS1U1B1XS1U1B0 = 20 - 0.5714QS1U1B1XS1U1B0.

Suppose That Three Consumers Are in the Market for Good