Question

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?

Answer 1

(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

Step-by-step explanation:

q=
`S^(1/2)`
`J^(1/2)` =
`√(SJ)`

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 =
`√(900J)`

q=
`√(900)` ×
`√(J)`

q = 30 ×
`√(J)`

`(q)/(30)` =
`√(J)`, squaring both sides we have,

(
`(q)/(30)`)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 = (
`(150)/(30)`)² = 5²

J = 25

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

(b) (
`(q)/(30)`)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(
`(q)/(30)`)²

Marginal cost, MC =
`(dC)/(dq)`

=
`(d)/(dq)` [$2,700 + $12(
`(q)/(30)`)²]

=
`(4q)/(150)`

if q = 150, MC =
`(4*150)/(150)`

= $4

if q = 300, MC =
`(4*300)/(150)` = $8