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=S1/2J1/2 Where q is the number of pages in the finisjed book, S is the number of working hours spent by Smith, and J is the number of working hours spent by Jones. After having spent 900 hours preparing the first draft, time which he valued at $3 per working hour, Smith has to move on to other things and cannot contribute any more to the book. Required:
a. How many hours will Jones have to spend to produce a finished book of 150 pages? Of 300 pages? Of 450 pages?
b. What is the marginal cost of the 150th page of the finished book? Of the 300th page? Of the 450th page?

Answer 1

The time taken that Jones will spend to produce a finished book of 150 pages is 25 hours.

How to calculate the time taken?

The number of hours to produce a finished book of 150 pages will be:

q = ✓SJ

150 = ✓900 × ✓J

J = 150²/30²

J = 25

The number of hours to produce a finished book of 300 pages will be:

J = (300)² / 30²

= 100

The number of hours to produce a finished book of 450 pages will be:

= 450² / 30²

= 225 hours.

The marginal cost of the 150th page of the finished book will be:

= 4q/150

= (4 × 150)/150

= 4

The marginal cost of the 300th page of the finished book will be:

= (4 × 300)/150

= 8

The marginal cost of the 450th page of the finished book will be:

= (4 × 450) / 150

= 12

In conclusion, the marginal cost of the 450th page is $12.

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