Question

A factory produces 7,000 units of car replacement component per month which can be sold at the price of $50/unit. The monthly labor cost is $1,000 per worker with 8 workers available, material cost is $5,000, and overhead cost is 20% of the material cost. A new machine can be added that will increase the output by 1000 units, decrease the number of workers by one, and increase the overhead cost by $3000. Compute the productivity growth and justify whether the addition of the new machine is beneficial or not

Answer 1

Before addition of new machine

Total cost (Input) = Labor cost + Material cost + Overhead cost

= 1000 + 5000 + 5000*0.2

= $ 7000

Output = 7000 units

Productivity = Output / Input = 7000 units / $ 7000

= 1 unit / $

After addition of new machine

Total cost (Input) = Labor cost + Material cost + Overhead cost

= 1000*7/8 + 5000 + 5000*0.2+3000

= $ 9875

Output = 8000 units

Productivity = Output / Input = 8000 units / $ 9875

= 0.81 unit / $

Productivity growth = (0.81-1)/1 = -19 % (minus sign indicates de-growth)

We see that after the addition of new machine, productivity has shrunk, instead of growing.

Therefore, addition of new machine is not beneficial in terms of productivity improvement.