Question

2. A publisher brings a new book on the market. The demand for the book is q = 500−10pwhere q denotes quantity and p price. The publisher has to pay an initial cost of $100 to be able to print the book, and the printing of each book costs $1.

   1. (a) What is the total revenue of the publisher depending on the number of books sold?

   2. (b) What is the total cost of the publisher depending on the number of books sold?

   3. (c) What does the marginal revenue measure? Calculate the marginal revenue for 1,2,3 and 4 books produced.

   4. (d) Which two effects result in monopolist?s marginal revenue being smaller than the demand? Which of the two effects is absent under perfect competition and why?

Answer 1

a) Q=500-10p

P=50-0.1q

Total revenue= P*Q= (50-0.1q)*q= 50q-0.1q^2

b) Total cost= 100+1*q=100+q

c) Marginal revenue measures the additional revenue earned by producing one more unit of the book.

Total revenue= 50q-0.1 q^2

Differentiate TR with respect to q to find MR.

MR=dTR/dq= 50-0.2q

When q=1, MR= 50-0.2=49.8

When q=2,MR= 50-0.4=49.6

When q=3, MR= 50-0.6=49.4

When q=4, MR =50-0.8= 49.2

D) Demand curve is downward sloping for monopolist.

Selling another unit raises the revenue by the new lower price level. This effect is also there under perfect competition.

Another effect under monopolist that is absent under perfect competition is that - To sell more the monopolist has to reduce the prices on all the previous units sold. So the revenue from these units falls. Under perfect competition the marginal revenue is equal to price and is constant for all the units sold.