Question

$\mathit{T}\mathit{h}\mathit{e}\mathbf{}\mathit{e}\mathit{l}\mathit{a}\mathit{s}\mathit{t}\mathit{i}\mathit{c}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{d}\mathit{e}\mathit{m}\mathit{a}\mathit{n}\mathit{d}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathit{a}\mathbf{}\mathit{f}\mathit{i}\mathit{r}\mathit{m}\mathbf{’}\mathit{s}\mathbf{}\mathit{p}\mathit{r}\mathit{o}\mathit{d}\mathit{u}\mathit{c}\mathit{t}\mathbf{}\mathit{i}\mathit{s}$$\mathbf{2}\mathbf{.}\mathbf{5}$$\mathit{a}\mathit{n}\mathit{d}\mathbf{}\mathit{i}\mathit{t}\mathit{s}\mathbf{}\mathit{a}\mathit{d}\mathit{v}\mathit{e}\mathit{r}\mathit{t}\mathit{i}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathit{e}\mathit{l}\mathit{a}\mathit{s}\mathit{t}\mathit{i}\mathit{c}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{d}\mathit{e}\mathit{m}\mathit{a}\mathit{n}\mathit{d}$is localid="1653547180528" $\mathbf{0}\mathbf{.}\mathbf{2}$.

$\mathit{a}\mathbf{.}\mathbf{}\mathit{D}\mathit{e}\mathit{t}\mathit{e}\mathit{r}\mathit{m}\mathit{i}\mathit{n}\mathit{e}\mathbf{}\mathit{t}\mathit{h}\mathit{e}\mathbf{}\mathit{f}\mathit{i}\mathit{r}\mathit{m}\mathbf{’}\mathit{s}\mathbf{}\mathit{o}\mathit{p}\mathit{t}\mathit{i}\mathit{m}\mathit{a}\mathit{l}\mathbf{}\mathit{a}\mathit{d}\mathit{v}\mathit{e}\mathit{r}\mathit{t}\mathit{i}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathbf{-}\mathit{t}\mathit{o}\mathbf{-}\mathit{s}\mathit{a}\mathit{l}\mathit{e}\mathit{s}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathbf{.}$

$\mathit{b}\mathbf{.}\mathbf{}\mathit{I}\mathit{f}\mathbf{}\mathit{t}\mathit{h}\mathit{e}\mathbf{}\mathit{f}\mathit{i}\mathit{r}\mathit{m}\mathbf{’}\mathit{s}\mathbf{}\mathit{r}\mathit{e}\mathit{v}\mathit{e}\mathit{n}\mathit{u}\mathit{e}\mathit{s}\mathbf{}\mathit{a}\mathit{r}\mathit{e}$$\mathbf{40}\mathbf{,}\mathbf{000}$$\mathbf{,}\mathbf{}\mathit{w}\mathit{h}\mathit{a}\mathit{t}\mathbf{}\mathit{i}\mathit{s}\mathbf{}\mathit{i}\mathit{t}\mathit{s}\mathbf{}\mathit{p}\mathit{r}\mathit{o}\mathit{f}\mathit{i}\mathit{t}\mathbf{-}\mathit{m}\mathit{a}\mathit{x}\mathit{i}\mathit{m}\mathit{i}\mathit{z}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathit{l}\mathit{e}\mathit{v}\mathit{e}\mathit{l}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{a}\mathit{d}\mathit{v}\mathit{e}\mathit{r}\mathit{t}\mathit{i}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathbf{?}$

Short answer

a. The firm's optimal advertising-to-sales ratio is 0.08.

b. The firm's profit-maximizing level of advertising for a $40000revenue is $3200.

Step-by-step solution

Determining the firm’s optimal advertising-to-sales ratio

a.

Let$E_{QP}$ represent the price elasticity of demand.

$E_{Q,P}=‐2.5$

Let $E_{QA}$represent the advertising elasticity of demand.

$E_{Q,A}=0.2$

Using the profit-maximizing advertising-to-sales ratio formula, we get

_{.$\frac{A}{R}=\frac{E_{Q,A}}{-E_{Q,P}}$}

Substituting the values $E_{QP}=-2.5$and $E_{QP}=0.2$in the equation, we get

_{.$$\begin{gathered} \frac{A}{R}=\frac{0.2}{-\left(-2.5\right)} \\ =\frac{0.2}{2.5} \\ =0.08 \end{gathered}$$}

Hence, the firm's optimal advertising-to-sales ratio is 0.08.

Determining the firm's profit-maximizing level of advertising

b.

Let R represent the firm's revenue. So, R=40000.

Using the result from Part a), we get

_{.$$\begin{gathered} \frac{A}{R}=0.08 \\ \frac{A}{40000}=0.08 \\ A=3200 \end{gathered}$$}

Thus, the firm's profit-maximizing level is $3200.