# marginal cost

I. - Professor Smith and Professor Jones are going to produce a new introductory textbook. Production Function : q = (SJ)1/2

Q = number of pages in finished book

S = number of working hours spent by Spent

J = number of working hours spent by Jones

Smith values labor at $20 per working hour, she spent 900 hours providing the first draft. Jones, labor valued at $80 per working hour will revise Smith's draft.

(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?

ii. - Suppose a firm's constant-return-to-scale production function requires it to use capital and labor in a fixed ratio of two workers per machine to produce 10 units and that the rental rates for capital and labor are given by v = 1 and w = 3.

a. Calculate the firm's long-run total and average costs curves.

b. Suppose K is fixed at 10 in the short run. Calculate the firm's short-run total and average cost curves. What is the marginal cost of the 10th, 25th, 50th, and 100th unit?

#### Solution Preview

i.(a) How many hours will Jones have to spend to produce a finished book of 150 pages? Of 300 pages? Of 450 pages?

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<br>Since S=900, from q = (900J)^0.5 = 30 J^0.5

<br>We can write J = (q/30)^2

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<br>Then when q=150, J =(150/30)^2 = 25

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<br>Then when q=300, J =(300/30)^2 = 100

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<br>Then when q=450, J =(450/30)^2 = 225

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<br>(b) What is the ...

#### Solution Summary

Calculate the firm's short-run total and average cost curves.