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If employees’ salaries are increased by 20%, what is the increase in productivity required to break even?

Can someone assist me in solving this question?

Productivity = (output per period)/(number of employees)

How is productivity related to the employees salaries?

Thank you

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    $\begingroup$ This is at best part of a question. Without more details it is not possible to give a satisfactory answer. $\endgroup$ – Giskard Dec 22 '19 at 9:31
  • $\begingroup$ Giskard, it is a potential case question for a consulting interview, I am supposed to ask the interviewer for any information I need to be able to answer it. The break even point varies with the fixed costs, variable cost, and price charged for each unit. How are these three variables related to the emploees salaries, or productivity? $\endgroup$ – maths New Dec 23 '19 at 14:54
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Break even is when your [economic] profits equals to zero:

\begin{align*} \text{Cost} &= \text{Revenue}\\ N \cdot w &= Q \cdot P \end{align*}

where $N$ is the number of workers, $w$ is wages, $Q$ is quantity produced, and $P$ is price.

An $x$% increase in productivity is the ability to hire the same amount of workers and get $x$% more output.

Assume that $N$ and $P$ remains unchanged, a 20% increase in wages would lead to the LHS's being $L \cdot 1.2w$ instead. How would the RHS need to change to maintain equality?

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    $\begingroup$ Why does Cost= N*w ? Wage is just a part of the fixed costs. Isn't cost= Fixed Cost+ Variable costs? $\endgroup$ – maths New Dec 27 '19 at 6:18
  • $\begingroup$ Here I'm making a simplifying assumption that labor cost is the only cost involved. It doesn't really matter whether wage is fixed cost or variable cost. The only thing that simplifies it is that wage is the only cost. The problem would get more complicated with other fixed costs, and even more complicated with other variable cost. $\endgroup$ – Art Dec 27 '19 at 7:14

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