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

The monopolist can calculate the projected increase in total revenue after a 10% price increase by understanding that with a price elasticity of demand of -0.5, total revenue will increase as the loss in quantity sold is proportionally smaller than the gain from the higher price, leading to an increase in total revenue from $10,000 to $10,450.

Step-by-step explanation:

The question involves calculating the effect of a price change on total revenue, given the price elasticity of demand. The price elasticity of demand is a measure used to show the responsiveness, or elasticity, of the quantity demanded of a good or service to a change in its price. The monopolist is considering raising the price of textbooks by 10%, knowing that the price elasticity of demand is -0.5, which indicates that demand is inelastic. In such a case, the increase in price will lead to a smaller percentage decrease in quantity demanded, thus allowing total revenue to increase. An elasticity of -0.5 means that for every 10% increase in price, the quantity demanded decreases by only 5%. Therefore, the new revenue will be higher than the initial $10,000.

To compute the projected total revenue after a 10% price increase:

1. Calculate the new price: $100 + (10% of $100) = $110.
2. Calculate the percentage change in quantity demanded: 10% price increase × -0.5 elasticity = -5% change in quantity demanded.
3. Calculate the new quantity demanded: 100 books minus (5% of 100 books) = 95 books.
4. Calculate the new total revenue: 95 books × $110 per book = $10,450.

By increasing the price, total revenue would increase from $10,000 to $10,450, assuming the elasticity remains constant over the price range.

Answer 2

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