(Solved):   1) Professor Smith and Professor Jones are going to produce a new introductory textbook, a ...

 

1) Professor Smith and Professor Jones are going to produce a new introductory textbook, as true economists they have laid out the production function for the textbook as \[ q=\sqrt{S J} \] where \( q= \) the number of pages in the finished book, \( S= \) the number of working hours spent by Smith, and \( \mathrm{J}= \) the number of working hours spent by Jones. Smith values her labor as \$20 per working hour. She has spent 900 hours preparing the first draft. Jones, whose labor is valued at \( \$ 80 \) 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? Of 300 pages? Of 450 pages? b. What is the marginal cost of the 150 th page of the finished book? Of the 300 th page? Of the 450 th page? 2) Consider the following production function: \[ q=5 \sqrt{K L} \] Where \( \mathrm{K} \) is capital and \( \mathrm{L} \) is labor. The cost of capital is \( \$ 100 \) /unit, and the cost of labor is \$25/unit. On a single graph, draw (use Excel or similar software) the short run average total cost function when capital is fixed at 100 units, the short run average total cost function when capital is fixed at 225 units and the short run average total cost function when capital is fixed at 400 units. If these are the only choices for capital, over what range of output will the firm choose 100 units of capital, 225 units of capital, 400 units of capital?