Professor Smith and Professor Jones are going to produce a new introductory textbook. As true scientists, they have laid out the production function for the book as q=S1/2J1/2q=S1/2J1/2, where q = the number of pages in the finished book, S = the number of working hours spent by Smith, and J = the number of hours spent working by Jones. After having spent 900 hours preparing the first draft, time that he valued at $3 per working hour, Smith has to move on to other things and cannot contribute any more to the book. Jones, whose labor is valued at $12 per working hour, will revise Smith's draft to complete the book. a. How many hours will Jones have to spend to produce a finished book of 150 pages? b. What is the marginal cost of the 150th page of the finished book? Of the 300th page?

(a) It will take Jones 25 hours to produce a finished book of 150 pages

(b) The marginal cost of the 150th page of the finished book is $4

The marginal cost of the 300th page of the finished book is $8

Explanation:

q= =

q = the number of pages in the finished book

S = the number of working hours spent by Smith

J = the number of hours spent working by Jones.

For first draft, smith works for 900 hours at $3 per working hour

q =

q= ×

q = 30 ×

= , squaring both sides we have,

()² = J

(a) Since Jones has to produce a book of 150 pages and Smith worked 900 hours on it,

q = 150, S = 900 , J = ?

J = ()² = 5²

J = 25

Therefore, it would take 25 hours for Jones to produce a book of 150 pages.

(b) ()² = J

Since Smith worked for 900 hours at $3 per working hour, his total cost of work is = 900 × $3 = $2,700.

Jones total cost of work  at $12 per working hour = $12J

Total cost of work, C = $2,700 + $12J

C = $2,700 + $12()²

Marginal cost, MC =

= [$2,700 + $12()²]

=

if q = 150, MC =

= $4

if q = 300, MC = = $8

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