The Truck Outfitters (TTO) sells truck accessories to retailers from coast to co

Question

The Truck Outfitters (TTO) sells truck accessories to retailers from coast to coast. One of the products TTO sells is a seat cover that sells for $8.00 per piece. TTO's production function is given by the expression: Q = 80L – 0.5L2, where

   Q = number of seat covers per day, and
   L = number of skilled workers per day.

Based on this production function, the average and marginal products of labour are as follows:

   AP = 80 – 0.5L and MP = 80 – L

a) If TTO pays $120 per day for each of its skilled workers, how many workers should the firm employ?

b) TTO's workers are highly skilled with a great deal of job mobility. The firm's managers fear that they must increase the workers' total compensation to $160 per day to remain competitive. What impact would the wage increase have upon the firm's employment?

Explanation / Answer

Profit Function=Revenue-Cost

Revenue=Price per seat* Output=8*(80L-0.5L^2)=640L-4L^2

Cost=wL & w=$120

Profit=640L-4L^2-120L

=520L-4L^2

Now we need to find optimum level of Labor for that we need to find FOC and equal to zero

d(Profit)/dL=520-8L=0

L=65

Ans b)

Now if Wage is increased to $160 then Profit

Revenue=Price per seat* Output=8*(80L-0.5L^2)=640L-4L^2

Cost=wL & w=$160

Profit=640L-4L^2-160L=480L-4L^2

follwoing the same process

d(Profit)/dL=480-8L=0

hence L=60

Therefore we can say that as wage increases from $120 to $160 labour employnebt decreases from 65 to 60

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