(a)

Average productivity of the workforce is .

Where is total value of production and is number of workers in plant.

Marginal cost function is the derivative of cost function.

Consider .

Differentiate on each side with respect to .

.

Quotient rule of derivatives: .

When , then

From the above expression total production is directly proportional to the total number of workers.

So if productivity increases, then the number of workers also increases.

(b)

.

If ,

Substitute in above expression.

.

Thus, if is greater than the average productivity, then .   

(a) .

(b) , if  is greater than the average productivity.