The number of workers increased by 25% , and output (total product) by 75% Determine how much labor productivity changed (in percent)?

To determine the change in labor productivity, we need to calculate the percentage change in output per worker.<br /><br />Let's assume the initial number of workers is $W_1$ and the initial output is $Q_1$. After the increase, the number of workers becomes $W_2 = 1.25W_1$ and the output becomes $Q_2 = 1.75Q_1$.<br /><br />Labor productivity is defined as the output per worker. Therefore, the initial labor productivity is $LP_1 = \frac{Q_1}{W_1}$ and the new labor productivity is $LP_2 = \frac{Q_2}{W_2}$.<br /><br />To find the percentage change in labor productivity, we can use the formula:<br /><br />Percentage change in labor productivity = $\frac{LP_2 - LP_1}{LP_1} \times 100\%$<br /><br />Substituting the values, we get:<br /><br />Percentage change in labor productivity = $\frac{\frac{1.75Q_1}{1.25W_1} - \frac{Q_1}{W_1}}{\frac{Q_1}{W_1}} \times 100\%$<br /><br />Simplifying the expression, we have:<br /><br />Percentage change in labor productivity = $\frac{1.75 - 1}{1} \times 100\%$<br /><br />Percentage change in labor productivity = $0.75 \times 100\%$<br /><br />Percentage change in labor productivity = $75\%$<br /><br />Therefore, the labor productivity increased by $75\%$.