Question

8. You are the manager in charge of monitoring cash flow at a company that makes photography equipment. Traditional photography equipment comprises 80 percent of your revenues, which grow about 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 -0.2. In 2009, your company earned about $400 million from sales of digital cameras and about $600 million from sales of disposable cameras.

Using the information above, if the own price elasticity of demand for disposable cameras is -2.5, how will a 1 percent decrease in the price of disposable cameras affect your overall revenues from both disposable and digital camera sales? In your answer compute:

a. The change in revenues in dollars from the resulting sale of disposable cameras after the 1 percent decrease in
     the price of disposable cameras.

b. The change in revenues in dollars from the resulting sale of digital cameras after the 1 percent decrease in the
   price of disposable cameras.

c. The total effect on sales for the company after the 1 percent decrease in the price of disposable cameras.

Answer 1

(a)

Own-price elasticity for disposable camera = % Change in quantity of disposable camera / % Change in its own price

-2.5 = % Change in quantity of disposable camera / (-1%)

% Change in quantity of disposable camera = (-2.5) x (-1%) = 2.5%

New quantity of disposable camera = Original quantity x 1.025

Initial revenue = P x Q = $600 million

New revenue = New price x New quantity = (P x 0.99) x (Q x 1.025) = (0.99 x 1.025) x (PQ) = 1.01475 x $600 million

= $608.85 million

(b)

Cross-price elasticity with digital camera = % Change in quantity of digital camera / % Change in price of disposable camera

-0.2 = % Change in quantity of digital camera / (-1%)

% Change in quantity of digital camera = (-0.2) x (-1%) = 0.2%

New quantity of disposable camera = Original quantity x 1.002

Initial revenue from digital camera = P x Q = $400 million

New revenue = New price x New quantity = (P x 0.99) x (Q x 1.002) = (0.99 x 1.002) x (PQ) = 0.99198 x $400 million

= $396.792 million

(c)

Initial total sales ($ million) = 600 + 400 = 1,000

New total sales ($ million) = 608.85 + 396.792 = 1,005.642

Net increase in revenue ($ million) = 1,005.642 - 1,000 = 5.642