Factor Demand Curve

Factor demand curve example

The factor demand curve below shows the demand for labor at a coffee processing company. The horizontal axis shows the number of workers (employment) whereas the vertical axis shows the wages. These represent the quantity demanded of the factor and the factor prices respectively. The curve shows that the company is willing to pay 1 worker $65. However, the factor price decreases by $10 with the addition of each worker until 7 workers receive just $5 each. This is because the more workers the company adds, the less the contribution of each worker to total production will be.

Fig. 2 - Example Labor Demand Curve

Determinants of factor demand curve

Determinants of the factor demand curve cause movements or changes in the factor demand curve. These are explained below.

Changes in the price of a product and shifts in the factor demand curve

How is the change in the price of goods a determinant of the factor demand curve?

Factor demand is a derived demand. This means that when there is a change in the price of a product whose production is dependent on a factor, the marginal revenue acquired from the product will change - consequently, the marginal revenue product of the factor will also change. Here, an increase in the price of the product will cause the factor demand curve to shift upward, and a decrease will cause it to shift downward. The following example will make things even clearer.

Changes in the supply of other factors and shifts in the factor demand curve

How is the change in the supply of other factors a determinant of the factor demand curve? Let’s look at the following example.

Fig. 3 - A Shift in the Labor Demand Curve

Changes in Technology and shifts in the factor demand curve

Generally, an increase or decrease in technological advancement does not have a set corresponding change in the demand of a factor. Rather, it is on a case-by-case basis. Simply put, depending on the specific technological advancement being increased, there could be either a decrease or an increase in the demand for a factor. Consider the following examples.

In both examples, there was a technological advancement, however, the resulting changes in factor demand were different.

Factor demand curve and marginal revenue product

Marginal productivity and marginal revenue product are important concepts when it comes to calculations involving the factor demand curve. Let's look at it in detail.

Factor Demand Curve: Marginal productivity of a factor of production

Fundamentally, any economic decision is made by comparing costs and their relative benefits. Usually, this is done by considering marginal costs and their relative marginal benefits. Let’s look at a simple example.

Factor Demand Curve: Marginal revenue product of a factor of production

The marginal cost of adding one more employee is the wage of that employee. However, what is the benefit of adding this employee? Well, there is the marginal product of a factor of production (i.e. the direct output that was produced following the addition of this factor), and there is marginal revenue product. Marginal revenue product represents the extra revenue generated from an extra factor of production (in the example of employees that is labor).

To calculate the marginal product of a factor of production you can use the following formula:

$MPF=\frac{Changeintotaloutput}{Changeintheproductionfactoremployed}=\frac{\Delta Y}{\Delta F}$

To calculate the marginal revenue product (MRP) of a factor of production you can use the following formula:

$MRPF=\frac{Changeintotalrevenue}{Changeintheproductionfactoremployed}=\frac{\Delta TR}{\Delta F}$

Factor Demand Curve: Marginal revenue product of labour

Using labor, the marginal revenue product of labor Is denoted by MRPL.

The calculation is really simple. Let’s break things down.

Consider a firm that is contemplating whether to employ an additional worker. The wage rate, denoted by W, is the marginal cost of hiring the additional worker. If the firm hires this additional worker, the added productivity will be the marginal product of labor, denoted by MPL. The additional output that was produced as a result of adding the new worker is the marginal product, denoted by MP. When the firm sells this marginal product, the revenue generated is referred to as the marginal revenue, denoted by MR.

Based on this, the formula for marginal revenue product of labor is the marginal product of labor multiplied by the marginal revenue:

For a firm to employ an additional unit of labor, the marginal revenue product of labor is equated to the marginal cost such that:

This is because naturally, the firm wants to at least break even. Therefore, the marginal revenue product of labor must at least be equal to the marginal cost for the firm to consider hiring the extra worker. In other words, marginal revenue product of labor should be equal to the wage rate.

Marginal revenue product and factor demand curve

Knowing what we know about the marginal revenue product of labor now, let's finish by illustrating this in Figure 4.

Fig. 4 - Marginal Revenue Product of Labor Curve

Notice the curve above looks exactly the same as the factor demand curve for labor.