Transcript 投影片 1 - National Tsing Hua University

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 q  SJ
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.
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 ?
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
8.7 Venture capitalist Sarah purchases two firms to produce widgets. Each
firm produces identical products and each has a production function
given by qi  Ki Li where i  1, 2
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 MPL  5/(2 L ) for firm 1, and MPL  5/( L ) for firm
2. Rental rates for K and L are given by     $1
a.
b.
c.
d.
If Sarah wishes to minimize short-run total costs of widget production,
how would output be allocated between the two firms?
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?
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.
How would your answer to part c change if both firms exhibited
diminishing returns to scale?
RTS=K/L=W/V for constant returns to scale