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You are a manager in charge of monitoring cash flow at a major publisher. Paper books comprise 80 percent of your revenues, which grow about 2 percent annually. You recently received a preliminary report that suggests the growth rate in ebook reading has leveled off, and that the cross-price elasticity of demand between paper books and ebooks is −0.2. In 2019, your company earned about $150 million from sales of ebooks and about $600 million from sales of paper books.


If your data analytics team estimates the own price elasticity of demand for paper books is −2.5, how will a 1 percent decrease in the price of paper books affect your overall revenues from both paper books and ebooks sales?

(I keep getting 14.7 million but the assignment says that is incorrect)

Sagot :

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Answer:

To calculate the change in overall revenues from both paper

books and ebooks sales due to a 1 percent decrease in the

price of paper books, we need to follow these steps:

1. Calculate the new price of paper books after a 1 percent

decrease:

Let the original price of paper books be denoted by P.

After a 1 percent decrease, the new price (P') will be:

P= P– 0.01P= 0.99P

2. Calculate the percentage change in quantity demanded of

paper books:

Given that the ovwn price elasticity of demand for paper books is

-2.5, we use the formula:

Eạ =

%AQa

%AP

Given that Eạ = -2.5, and we want to find the percentage

change in quantity demanded when the price decreases by 1

percent, we substitute the values:

-2.5 – %AQa

-1

3. Calculate the percentage change in quantity demanded of

ebooks:

Using the cross-price elasticity of demand between paper

books and ebooks (-0.2), we can calculate the percentage

change in quantity demanded of ebooks when the price of

paper books decreases by 1 percent:

%AQebooks = Cross-price elasticity x %AP = -0.2 x -1 = 0.2%

4. Calculate the change in revenues for both paper books and

ebooks:

The change in revenue for paper books will be:

Change in revenue from paper books = %AQax%APxOriginal revenı

Change in revenue from ebooks = %AQebooks X %AP x Revenue fromn

5. Add the changes in revenues from paper books and ebooks

to find the overall change in revenues.

This step-by-step process should help you accurately

determine how a 1 percent decrease in the price of paper books

will affect your overall revenues from both paper books and

ebooks sales.

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