Question

2. A publisher brings a new book on the market. The demand for the book is q = 500 - 10p where 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. (a) What is the total revenue of the publisher depending on the number of books sold? (b) What is the total cost of the publisher depending on the number of books sold? (c) What does the marginal revenue measure? Calculate the marginal revenue for 1,2,3 and 4 books produced. (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

Solution:

We are given the demand function for the book as: q = 500 - 10p

Then, the inverse demand function becomes: p = (500 - q)/10

Inverse demand function: p = 50 - 0.1*q

Further, price is p; initial cost (kind of a fixed cost) = $100; additional cost for each book (variable or marginal cost) = $1

(a) The number of books sold or the quantity of books sold is denoted by q. Total revenue = price*quantity

TR = p*q

TR = (50 - 0.1*q)*q (using the inverse demand function)

TR = 50q - 0.1q²

(b) Total cost is sum of all fixed costs (independent of quantity sold) and variable cost (those which depend on quantity level)

We have already established that variable cost of each book = $1, so total variable cost (for q books) = $1*q = q

Thus, total cost = total fixed cost + total variable cost

TC = 100 + q

(c) Marginal revenue is simply a measure of the additional revenue the producer earns by increasing the books sold by an additional unit.

Also, then marginal revenue is change in total revenue when quantity sold is increased by 1. So, MR = $\partial TR/\partial q$

So, MR = 50*1 - 2*0.1*q

MR = 50 - 0.2q

So marginal revenue when:

q = 1, MR = 50 - 0.2*1 = $49.8

q = 2, MR = 50 - 0.2*2 = $49.6

q = 3, MR = 50 - 0.2*3 = $49.4

q = 4, MR = 50 - 0.2*4 = $49.2

(d) Marginal revenue is smaller than the demand due to price effect and output effect. Output effect occurs as monopolist when sells more output, obviously the total output increases. However now at higher q level, price decreases (due to law of demand), so the price decreases on additional output (so marginal revenue decreases as output increases), and this lower price is charged for all initial output levels as well. This is the price effect.

Among the two, price effect is missing in competitive firm, as under perfect competition, firm being a price taker, the price they charge is nearly fixed. So no matter how many additional units are sold, price remains same.