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b. TC=P S S+P J J=40*900+80J=36000+80J q=30J 1/2 then J=q 2 /900

8.6 Professor Smith and Professor Jones are going to produce a new economics textbook. As true economists, they have laid out the production function for the book as where q = the number of pages in the finished books

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b. TC=P S S+P J J=40*900+80J=36000+80J q=30J 1/2 then J=q 2 /900

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  1. 8.6 Professor Smith and Professor Jones are going to produce a new economics textbook. As true economists, they have laid out the production function for the book as where q = the number of pages in the finished books S = the number of working hours spent by Smith J = the number of working hours spent by Jones Smith, the less experienced of the two, values her labor at $40 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. • How many hours will Jones have to spend to produce a finished book of 150 pages ? Of 300 pages ? Of 450 pages ? • What is the marginal cost of the 150th page of the finished book ? Of the 300th page ? Of the 450th page ?

  2. b. TC=PSS+PJJ=40*900+80J=36000+80J q=30J1/2 then J=q2/900 TC=36000+80*q2/900=36000+8q2/90 MC=16q/90 If q=150 then MC=80/3 If q=300 then MC=160/3 If q=450 then MC=80

  3. 8.7 Venture capitalist Sarah purchases two firms to produce widgets. Each firm produces identical products and each has a production function given by where The firms differ, however, in the amount of capital equipment each has. In particular, firm 1 has K1=25, whereas firm 2 has K2=100. The marginal product of labor is for firm 1, and for firm 2. Rental rates for K and L are given by a. If Sarah wishes to minimize short-run total costs of widget production, how would output be allocated between the two firms? b. Given that output is optimally allocated between the two firms, calculate the short-run total and average cost curves. What is the marginal cost of the 100th widget? The 125th widget? The 200th widget? c. How should Sarah allocate widget production between the two firms in the long run? Calculate the long-run total and average cost curves for widget production. d. How would your answer to part c change if both firms exhibited diminishing returns to scale?

  4. RTS=K/L=W/V for constant returns to scale

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