Question

You are a manager in charge of monitoring cash flow at a company that makes photography equipment. Traditional photography equipment comprises $\mathbf{40}$percent of your revenues, which grow about $\mathbf{2}$ percent annually. You recently received a preliminary report that suggests consumers take three times more digital photographs than photos with traditional film, and that the cross-price elasticity of demand between digital and disposable cameras is -0.3. In 2012, your company earned about #600 million from sales of digital cameras and about $400 million from sales of disposable cameras. If the own price elasticity of demand for disposable cameras is -2, how will a 4 percent decrease in the price of disposable cameras affect your overall revenues from both disposable and digital camera sales?

Short answer

The overall change in the revenue is $\$23.2$million.

Step-by-step solution

Introduction

We use the following equation to find out variation in income of a business.

$\Delta R=\left[R_x\left(1+E_{Q_x,P_x}\right)+R_y{E}_{Q_y,P_x}\right]·\%\Delta P_x$

Find the overall revenue change

In the formula,

$\Delta R=\left[R_x\left(1+E_{Q_x,P_x}\right)+R_y{E}_{Q_y,P_x}\right]·\%\Delta P_x$

$R_x$is the revenues of the disposable cameras

$R_y$is the revenues of the digital camera

$E_{Q_x{P}_x}$is the own price elasticity

$\%\Delta P_x$is the change in the price of the disposable cameras.

Hence,

$\Delta R=\left[R_x\left(1+E_{Q_x,P_x}\right)+R_y{E}_{Q_y,P_x}\right]·\%\Delta P_x$

$=[400\text{million}·(1-2)+600\text{million}-(-0.3\left)\right]·-0.04$

$=(-400\text{million}-180\text{million})·-0.04$

$=-580\text{million}·-0.04$

$\Delta R=\$23.2\text{million}$

Therefore, the overall change in the revenue of both the disposable and digital cameras is $\mathbf{\$}\mathbf{23}\mathbf{.}\mathbf{2}\mathbf{}\mathit{m}\mathit{i}\mathit{l}\mathit{l}\mathit{i}\mathit{o}\mathit{n}$.