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: Q^F = 27 – 2.00 × P. Here, Q^F 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: Q^M = 30 – 1.00 × P. Here, Q^M 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: Q^T represents total, or aggregate, demand. Solve for the demand curve for prices less than $12.)

Q^T =________ - P_________

Answer 1

Ans.

The values given in the question are as-

Female customers demand function for roses=

QF = 27- 2.00P

Male customers demand function for roses=

QM= 30 - 1.00P

Now ,the combined demand curve for both the customers = aggregate demand of both the customers(QT) = QF + QM

QT = 27- 2.00P + 30 - 1.00P

QT = 57 - 3.00P

Which is the combined demand curve for both the customers.

Now for the price less than 12 , the demand curve solution as-

If p = 12

The demand will be as-

QT= 57 - 3(12) ..( by putting value in combined demand curve)

= 57 - 36

= 21 units

Therefore , for the price less than12 the demand will be more than 21 units as there is inverse relationship between price and demand.

Therefore for price , P<12

21<QT<57

( it will be less than 57 as price is never negative and it will not be 0 as well , as demand for roses can't be perfectly inelastic.)