Question

The firm's elasticity of demand for labor is -0.5. The firm sells its output at $20 per unit, and the wage rate is $15 per hour. Suppose the firm experiences an increase in productivity such that at every level of employment its output is 200 unitslhour greater than before. What will happen to the number of workers hired by the firm?

Answer 1

The firm's elasticity of demand for labor is given as -0.5 implying that a $1 increase in wage reduces the labor demand by 0.5 units. Following an increase in productivity marginal product of labor increases by 200 units of labor hours and the price of output is $20 per unit. Therefore, the marginal revenue product of labor or MRPL following an increase in labor productivity=($20*200)=$4000. Now, the firm would maximize its profit at the output level which corresponds to the equality between the wage rate and the price of each unit of output which is $20. Hence, the wage rate has to increase from $15 to $20 per hour. Thus, the percentage change in the wage rate, in this case=($20-$15)/$15=0.33 or 33%. The elasticity of labor demand can be mathematically denoted as Percentage change in labor demand divided by the percentage change in wage rate. Now, let's suppose that the percentage change in labor demand of the firm be x.

Therefore, based on the mathematical formula to calculate the elasticity of labor demand, it can be stated:-

x/0.33=-0.5

x=-0.165

Hence, the percentage change in the labor demand or total labor hours would be decreased by 0.165 or 16.5%.