Question

When trying to assess differences in her customers, Claire—the owner of Claire’s Rose Boutique—noticed a difference between 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: ${\mathbf{Q}}^{\mathbf{F}}\mathbf{=}\mathbf{24}\mathbf{-}\mathbf{2}\mathbf{P}$. Here,${\mathbf{Q}}^{\mathbf{F}}$is the quantity of roses demanded by a female customer, and Pis the price charged per rose. She determined that her male customers have the following demand curve for roses:${\mathbf{Q}}^{\mathbf{M}}\mathbf{=}\mathbf{27}\mathbf{-}\mathbf{P}$. Here,${\mathbf{Q}}^{\mathbf{M}}$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?).

Short answer

The market demand curve is$\mathrm{Q}=51-3\mathrm{P}$

Step-by-step solution

Given

Given, the demand curve for roses for women is,$Q^F=24-2P$

Here,

$Q^F$is the quantity of roses demanded by a female customer

$P$is the price of rose.

The demand curve for roses for men is,$Q^M=27-P$

Here,

$Q^M$is the quantity of roses demanded by the female customer.

$P$is the price of rose.

Finding the market demand curve

We will substitute the demand functions into the equation, we will get,

$\begin{array}{rcl}Q& =& Q^M+Q^F\\ & =& 27-P+24-2P\\ & =& 27+24-P-2P\\ & =& 51-3P\end{array}$

Therefore, the market demand curve is Q = 51 - 3P.