Question

Question: A retail store had sales of \(45,000 in April and \)56,000 in May. The store employs eight full-time workers who work a 40-hour week. In April the store also had seven part-time workers at 10 hours per week, and in May, the store had nine part-timers at 15 hours per week (assume four weeks in each month). Using sales dollars as the measure of output, what is the percentage change in productivity from April to May?

Short answer

Answer

The percentage change in productivity from April to March is 6.65 per cent

Step-by-step solution

Calculating productivity of April

$\begin{array}{rcl}\text{Productivity}& =& \frac{\text{Output} \text{in} \text{dollars}}{\text{Input} \text{in} \text{hours}}\\ & =& \frac{45000}{\left[\left(\left(8\times 40\right)+\left(7\times 10\right)\right)\times 4\right]}\\ & =& \frac{45000}{1560}\\ & =& 28.85 \text{dollars} \text{per} \text{hour}\\ & & \end{array}$

Calculating productivity of May

$\begin{array}{rcl}d\text{Productivity}& =& \frac{\text{Output} \text{in} \text{dollars}}{\text{Input} \text{in} \text{hours}}\\ & =& \frac{5600}{\left[\left(\left(8\times 40\right)+\left(9\times 15\right)\right)\times 4\right]}\\ & =& \frac{5600}{1820}\\ & =& 30.77 \text{dollars} \text{per} \text{hour}\\ & & \end{array}$

Calculating percentage change

$\begin{array}{rcl}\text{Percentage} \text{change}& =& \frac{\text{Difference} \text{of} \text{values}}{\text{Initial} \text{value}}\times 100\\ & =& \frac{30.77-28.85}{28.85}\times 100\\ & =& \frac{1.92}{28.85}\times 100\\ & =& 0.0665\times 100\\ & =& 6.65 \%\\ & & \end{array}$