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corie corie
wrote...
Posts: 767
6 years ago
The table below shows a firm's output per day for zero through six workers.    

      Q   L   
   0   0
   46   1
   84   2
   114   3
   136   4
   150   5
   156   6

The firm's demand and marginal revenue curves are:

   P = 50 - 0.125Q   MR = 50 - 0.25Q,       

where Q = daily sales, and P = output price.
a.   Determine the marginal product of labor for one through six workers.
b.   Determine the firm's marginal revenue product.
c.   How many workers should the firm hire if total wage costs including fringe benefits are $30 per hour?  (Each worker is employed for eight hours per day.)
Textbook 
Microeconomics

Microeconomics


Edition: 8th
Author:
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Replies
wrote...
6 years ago
a.       
Marginal product is change in total product from one more worker.

      Q   L   MP   
   0   0   —
   46   1   46
   84   2   38
   114   3   30
   136   4   22
   150   5   14
   156   6   6

b.       
MRP = MR ∙ MPL       
We must determine MR at levels of output corresponding to one through six workers.         

MR    =    50 - 0.25Q   =   
MR(46)    =    50 - 0.25(46)     =    38.50
MR(84)    =    50 - 0.25(84)     =    29.00
MR(114)    =    50 - 0.25(114)    =    21.50
MR(136)    =    50 - 0.25(136)    =    16.00
MR(150)    =    50 - 0.25(150)    =    12.50
MR(156)    =    50 - 0.25(156)    =    11.00

   MRP = MR ∙ MPL

      L   Q   MP   MR   MRP   
   1   46   46   38.50   1771
   2   84   38   29.00   1102
   3   114   30   21.50   645
   4   136   22   16.00   352
   5   150   14   12.50   175
   6   156   6   11.00   66

c.       
The firm would want to hire every worker whose MRP > W.  Thirty dollars per hour is $240 per day.  The firm would want to hire four workers.
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