Question

Last month you assumed the position of manager for a large car dealership.The distinguishing feature of this dealership is its “no hassle” pricing strategy; prices (usually well below the sticker price) are posted on the windows, and your sales staff has a reputation for not negotiating with customers. Last year, your company spent$\mathbf{\text{(2}}$million on advertisements to inform customers about its “no hassle” policy, and had overall sales revenue of$\mathbf{\text{)40}}$million. A recent study from an agency on Madison Avenue indicates that, for each$\mathbf{\text{3}}$percent increase in TV advertising expenditures, a car dealer can expect to sell$\mathbf{\text{12}}$percent more cars—but that it would take a $\mathbf{\text{4}}$percent decrease in price to generate the same$\mathbf{\text{12}}$percent increase in units sold. Assuming the information from Madison Avenue is correct, should you increase or decrease your firm’s level of advertising? Explain.

Short answer

The company should not increase its advertising expenses to obtain more precise statistics on the influence of advertising on vehicle sales.

Step-by-step solution

Determining the profit-maximizing

The decisions made by the firm regarding its investment in advertising to increase its sales can be determined with the profit-maximizing advertising-to-sales ratio (A/R) equation, which is the following.

$\frac{\text{A}}{\text{R}}\text{=}\frac{{\text{E}}_{\text{Q,A}}}{{\text{-E}}_{\text{Q,P}}}$

Here,

${\text{E}}_{\text{Q}}\text{a}$is the advertising elasticity of demand.

${\text{E}}_{\text{Q}}\text{p}$is the own-price elasticity of demand and is negative by the inverse demand function.

Aisthe advertising expense.

R is the firm revenue.

Elasticity of demand-advertising

The elasticity of demand advertising seeks to measure the impact of advertising spending on the quantities demanded. In this case, it is vehicles. Therefore, it can be calculated as the variations in the quantities demanded with respect to the variations in advertising spending. This can be observed in the following equation:

_{${\text{E}}_{\text{Q,A}}\text{=}\frac{\text{\%VariationinQuantityDemanded}}{\text{\%VariationinAdvertisingSpending}}$}

According to a study by an advertising agency, for every $3\%$ spent on advertising, sales increased $12\%$ _. Therefore, we can substitute this data in the previous equation.

$\begin{array}{c}{\mathrm{E}}_{\mathrm{Q},\mathrm{A}}=\frac{12\mathrm{\%}}{3\mathrm{\%}}\\ {\mathrm{E}}_{\mathrm{Q}:\mathrm{A}}=4\end{array}$

Calculating the elasticity

The price-demand elasticity will seek to measure the change in the quantities of vehicles demanded in the face of price changes. It will take a$4\%$ variation in the price of the vehicles to increase the units sold by $12\%$. Therefore,we can calculate the elasticity as follows:

${\mathrm{E}}_{\mathrm{Q},\mathrm{A}}=\frac{\mathrm{\%}\mathrm{Variation}\mathrm{in}\mathrm{Quantity}\mathrm{Demanded}}{\mathrm{\%}\mathrm{Variation}\mathrm{in}\mathrm{Sell}\mathrm{Price}}$

Substituting the values:

$\begin{array}{l}{\mathrm{E}}_{\mathrm{Q},\mathrm{A}}=\frac{12\mathrm{\%}}{4\mathrm{\%}}\\ {\mathrm{E}}_{\mathrm{Q},\mathrm{A}}=3\end{array}$

Obtaining the advertising-revenue

Having both elasticities, we can substitute their values in the equation to obtain the Advertising-Revenue ratio that optimizes the firm's profit:

$\frac{\mathrm{A}}{\mathrm{R}}=\frac{{\mathrm{E}}_{\mathrm{Q},\mathrm{A}}}{-{\mathrm{E}}_{\mathrm{Q},\mathrm{P}}}\frac{\mathrm{A}}{\mathrm{R}}=\frac{4\mathrm{\%}}{3\mathrm{\%}}=\frac{0.04}{0.03}=1.33$

Discussing increasing the expenses of advertising

With this result of the$\mathrm{A}/\mathrm{R}$ ratio,the firm should increase its advertising expenses by$133\mathrm{\%}$ or$(\mathrm{\$}40\mathrm{million}\mathrm{x}1.33=\mathrm{\$}53.2\mathrm{million})$_, which does not make much sense.

Therefore, the firm should not increase the expenses of advertising to have more accurate information on the impact of advertising on vehicle sales.