Question

When trying to assess differences in her customers, Claire – the owner of Claire’s Rose Boutique – noticed a difference in the typical demand of her female versus her male customers. In particular, she found her female customers to be more price sensitive in general. After conducting some sales analysis, she determined that her female customers have the following demand curve for roses: QF = 24 – 2.50 × P. Here, QF is the quantity of roses demanded by a female customer, and P is the price charged per rose. She determined that her male customers have the following demand curve for roses: QM = 28 – 1.50 × P. Here, QM is the quantity of roses demanded by a male customer. If two unaffiliated customers walk into her boutique, one male and one female, determine the demand curve for these two customers combined (i.e., what is their aggregate demand?). (Note: QT represents total, or aggregate, demand. Solve for the demand curve for prices less than $12.)

Answer 1

Maximum price a female is willing to pay when QF = 0 is 24 - 2.5P = QF = 0
So, 2.5P = 24
So, P = 24/2.5 = 9.6
Thus, females will not demand at a price above 9.6

Maximum price a male is willing to pay when QM = 0 is 28 - 1.5P = QM = 0
So, 1.5P = 28
So, P = 28/1.5 = 18.67
Thus, only males will demand at a price above 9.6 and below 12.

So, QT = QF + QM for 0 < P < 9.6
And QT = QM for 9.6 < P < 12

QF + QM = 24 - 2.5P + 28 - 1.5P = 52 - 4P

Thus, QT = 52 - 4P when 0 < P < 12
And, QT = 28 - 1.5P for 9.6 < P < 12