When trying to assess differences in her customers, Claire the owner of Claires

Question

When trying to assess differences in her customers, Claire the owner of Claires 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 = 26 3.00*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 = 29 2.00*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.)

Explanation / Answer

QT=29-2P+26-3P=55-5P

The female will purchase roses only till the price is $8 and the male till the price is $14.

For P<$12,

QT=55-5P for 0<P<$8

QT=29-2P for $8<P<$12 (note that the female demand functions in neglected here since it is negative)

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