Question

You are a division manager at Toyota. If your marketing department estimates that the semi-annual demand for the Highlander is$\mathit{Q}\mathbf{-}\mathbf{150}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{5}\mathit{P}$, what price should you charge in order to maximize revenues from sales of the Highlander?

Short answer

In order to maximize revenues from sales of the Highlander, the price charged will be $50,000.

Step-by-step solution

Given information

Given,

$Q=150,000-1.5P$

Find the price to be charged

By using the equation, we get the own price elasticity of demand:

$E_{Q_{x,}{p}_x}={\alpha }_x\frac{P_x}{Q_x}=-1$

By calculating we will get,

$$\begin{gathered} E_{Q_{x,}{p}_x}={\alpha }_x\frac{P_x}{Q_x}=-1 \\ =-1.5\frac{P_x}{150,000-1.5P}=-1 \\ {P}_x=\frac{-1}{-1.5}.\left(150,000-1.5P\right) \\ {P}_x=\frac{2}{3}\left(150,000=1.5P\right) \\ P=150,000-100,000 \\ P=50,000 \end{gathered}$$

Therefore, the price that should be charged, in order to maximize the revenues from the sales of the Highlander is $\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}$$\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}$