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

The demand for the book is q = 500 − 10p and so the inverse demand is 10p = 500 - q or p = 50 - 0.1q. There is a fixed initial cost of $100 and then a marginal cost of printing at MC = $1.

1. (a) Revenue function is R(q) = pq = (50 - 0.1q)q or R(q) = 50q - 0.1q^2

2. (b) Total cost of the publisher = 100 + q

3. (c) Marginal revenue measures the additional revenue received when one additional book is sold. Marginal revenue function has same intercept as inverse demand function but with twice the slope so MR = 50 - 0.2q. MR (q = 1) = 49.80, MR (q = 2) = 49.60, MR (q = 3) = 49.40, and MR (q = 4) = 49.20.

4. (d) Price effect and quantity effect. Since price is fixed in perfect competition there is only quantity effect.