Question

You are a monopolist who sells textbooks to undergraduate students. Currently you sell 100 books at a price of​ $100 each, for revenue of​ $10,000. Each book is essentially costless to​ print, so you ignore fixed costs and focus on maximizing revenue. Based on research by your marketing​ team, you learn that some students will not buy the book if the price goes up.​ Also, if you cut the​ price, more students will buy the book. Suppose the price elasticity of demand is​ -0.5. If the price of each textbook is increased by 10​ percent, the new revenue earned is ​$ nothing.

Answer 1

Given:

Old Price of book =P100

Let X= Change in quantity

Let Y= Change in Price (10%)

The formula for price elasticity is:

Price Elasticity = (% Change in Quantity) / (% Change in Price)

.50=X/Y

-.50=X/(10)

x/10=.50

X=.50(10)

X=5

Let Z=New Quantity Demanded

Z=100+.05(100)

Z=100+5

Z=105

Let A=New price

A= 100+.10(100)

A=100+10

A=110

New Total revenue =Z(A)

=105*110

=11,550