Chapter 11, Problem 1Q

To determine

The estimation process for the demand for labor.

Explanation of Solution

The demand for labor is estimated using three variables, namely marginal product of labor $\left(MPL\right)$, wage $\left(W\right)$, and price $\left(P\right)$ of the product in the existing market. The marginal product of labor refers to the additional output produced by hiring one additional worker.

Two important assumptions that are made while deriving the demand for labor are, the firm functions in a competitive market and the labor market is also competitive in nature. Second, the ‘Law of diminishing returns’ prevails, which means that the marginal value of labor starts to fall as more and more workers are hired.

To determine the number of workers employed at different wage rates, firstly, derive the value of marginal product of labor $\left(VMPL\right)$ which is equal to the product of marginal product of labor and price of the product in the market $\left(MPL\times P\right)$. The VMPL refers to the money value of the marginal product(MP) of labor, or, in other words, the extent to which an additional worker contributes to the firm in terms of money. The value of $VMPL$ differs at different levels of output due to the $MPL$ that works on the ‘Law of diminishing returns’.

The table below displays different variables at different levels of output and workers.

$\begin{array}{cccc}\text{Output per day}& \text{Number of workers}& \text{MPL}& \text{VMPL (at P = \$2)}\\ 0& 0& -& -\\ 100& 1& 100& 200\\ 200& 2& 90& 180\\ 300& 3& 85& 170\\ 350& 4& 75& 150\\ 400& 5& 65& 130\\ 425& 6& 50& 100\\ 450& 7& 45& 90\end{array}$

A profit-maximizing firm chooses the optimal number of workers to hire by determining what the value of the marginal product would be at the given wage rate for every additional worker hired. The firm will demand the amount of labor where $VMPL=W$.

If VMPL is higher than the existing wage rate at a particular number of workers, then the firm will have an incentive to hire an additional worker as the worker will be able to bring in more money for the firm than what they would have to pay. On the other hand, if $W$ is higher than $VMPL$ at a certain number of workers, then the firm would not hire the additional worker required to reach that level as they would have to pay the worker more than the additional money that the worker would have been bringing for the firm. Hence, the optimal level would be $VMPL=W$.

The demand for labor is determined by $VMPL=W$ at different number of workers employed. This is demonstrated (using the table) in the diagram given below.