# modelling Inconsistent production functions

last year I asked How do we estimate production functions?. That answer provided was insightful from an econometric perspective and has helped me in applying such an understanding to the workplace.

Right now Im doing some consulting by a small medical sales business and they wanted me to do a workforce evaluation of their sales staff, and they wanted to know if they should expand their workforce. The numbers they are giving me are on a monthly basis, they did not provide me with numbers of what their revenues are but they have given me quantities like the table below. (Note the numbers provided are fictitious).

\begin{array}{c|lcr|} n & \text{Sales}&\text{Staff}{} \\ \hline 1 &103& 10\\ 2 &234& 10\\ 3&88&9\\ 4 &115& 8 \\ 5&63&9\\ 6&91&10\\ 7&130&10\\ 8&168&9\\ ...&...&...\\ \end{array}

We know mathematically a production function provide us with a single value, however as we can see from this table, the quantities produced by the input above differs by time and period.

How does one model such inconsistencies in production where the exact yield from inputs are not specific.

• Are stocks of finished product sometimes carried over from one month to the next? If so then a first step would be to adjust the sales figures for stock carried over so as to obtain data for production. – Adam Bailey Nov 12 '17 at 13:16
• @AdamBailey I dont know if stock of finished products would matter here. I'm asking for how to calculate the sales maximizing number of staff when yields are not constant. – EconJohn Nov 12 '17 at 16:15