Mark writes a book on Bitcoin. The demand for the book is P=20-Q. The marginal c

Question

Mark writes a book on Bitcoin. The demand for the book is P=20-Q. The marginal cost is $2 per book. The total fixed cost is $10.

a. If all consumers pay the same price, at what price will he sell and what will be his profit?

b. Now assume Mark wants to sell the book as an ebook, downloadable from his website. Marginal cost in this case would be zero and it costs him nothing to run his website. He wants to give his friends the possibility of letting them pay whatever amount they want for the ebook. Since his friends love him so much, all pay their maximum willingness to pay. How much profit will he make in this case?

Explanation / Answer

(a) Profit is maximized by equating Marginal revenue (MR) with Marginal cost.

P = 20 - Q

Total revenue (TR) = P x Q = 20Q - Q2

MR = dTR / dQ = 20 - 2Q

Equating MR & MC,

20 - 2Q = 2

2Q = 18

Q = 9

P = 20 - 9 = $11

Profit ($) = Q x (P - MC) - Fixed cost = 9 x (11 - 2) - 10 = 9 x 9 - 10 = 81 - 10 = 71

(b) In this case, P = MC = 0 and Profit = Consumer surplus (CS)

From demand function, when Q = 0, P = $20 (Maximum willingness to pay) & When P = 0, Q = 20

Profit = CS = Area between demand curve and market price = (1/2) x $(20 - 0) x 20 = (1/2) x $20 x 20 = $200

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