Professor Bong has just written the first textbook in MicroEconomics. Market res

Question

Professor Bong has just written the first textbook in MicroEconomics. Market research suggests that the demand curve for this book will be Q = 2,000-100P, where P is its price. It will cost $1000 to set the book in type. This setup cost is necessary before any copies can be printed. In addition to the setup cost, there is a marginal cost of $4 per book for every book printed.

a) Find the total revenue function for Professor Bong's book (find R(Q))

b) Find the total cost function for producing Professor Bong's book (find C(Q)).

c) Find the marginal revenue function and the marginal cost function. Find the profit-maximizing quantity of books for Professor Bong to sell.

Thanks in advance!!

Explanation / Answer

a. P= (2000 - Q)/100 = 20 - Q/100

So R = PQ = 20Q - Q2/100

b. C = 1000 +4Q

c. Marginal Revenue = dR/dQ = 20 - 2Q/100 = 20 - Q/50

Marginal Cost = dC/dQ = 4

For max profit, MR=MC

or, 20 - Q/50 = 4

Q = 800

P = 12$

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