Question

At a certain factory, the daily output is Q(L) 60,000L13 units, where L denotes the size of the labor force measured in worker-hours. Currently 1,000 worker-hours of labor are used each day. Estimate the effect on output that will be produced if the labor force is cut to 940 worker-hours.

Answer 1

If the labor force is cut to 940 worker-hours, the factory will produce 12248 fewer units per day.

Estimating the effect on output if the labor force is cut

From the question, we have the following parameters that can be used in our computation:

`\text{Q(L)} = 60000L^\frac 13`

When there are 1000 worker hours of labor, we have

`\text{Q(1000)} = 60000 * (1000)^\frac 13`

Evaluate

Q(1000)} = 600000

If the labor force is cut to 940 worker-hours, we have the output to be

`\text{Q(940)} = 60000 * (940)^\frac 13`

Evaluate

Q(940) = 587752

So, we have

Reduction = 600000 - 587752

Reduction = 12248

Hence, the estimated effect on output is a reduction by 12248 units per day