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Factor Demand Curve

Why is it that sometimes firms hire new workers, but the total production begins to drop? How do firms decide to fire a lot of workers at once, and how do they decide on the wages of the new employees? As labour is one of the factors of production we need to relate it to the concept of factor demand. If you want to know how exactly to do that and want to be able to answer these questions, then this explanation will help you do so!

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# Factor Demand Curve

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Why is it that sometimes firms hire new workers, but the total production begins to drop? How do firms decide to fire a lot of workers at once, and how do they decide on the wages of the new employees? As labour is one of the factors of production we need to relate it to the concept of factor demand. If you want to know how exactly to do that and want to be able to answer these questions, then this explanation will help you do so!

## Factor demand curve meaning

Similar to the definition of goods demand, factor demand refers to the willingness and ability of a firm to purchase factors of production. So what is the factor demand curve? Simply put, the factor demand curve is the graphical representation of factor demand. But here is a more accurate definition.

The factor demand curve is the graphical illustration of the relationship between the price of a factor of production and the quantity demanded of that factor of production.

As the definition suggests, the factor demand curve is a graph. It shows the factor price on the vertical axis and the quantity demanded of the factor on the horizontal axis. The factor demand curve has a negative slope as higher factor prices come with lower quantities demanded. A simple labor demand curve is illustrated below in Figure 1.

Compared to the other factors of production, labor is more often analyzed since it deals directly with humans.

Fig. 1 - Labor 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.

The determinants of the factor demand curve are factors that cause the factor demand curve to shift. They include changes in the prices of products, the supply of other factors, and technology.

### 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.

Consider a market where the price of processed coffee increases. This means that the coffee processing plant will increase its supply. As the plant wants to increase supply, this will cause an increase in demand for coffee processing labor, and consequently, wages will increase. Therefore, the increase in the price of coffee causes the factor demand curve to shift upward.

### 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.

Consider the coffee processing plant with 7 employees. When the company acquires more land for growing coffee, each worker will process more coffee because there is more coffee from the extra land. This means that the marginal product of labor will increase at the various levels of employment (only 1 employee, only 2 employees, etc.). As a result, the factor demand curve for labor shifts upward as shown in Figure 3 below.

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.

Horses and oxen were once an important factor of production as they were the main form of transportation for farm produce. However, with the invention of cars, horses and oxen have declined in demand, shifting their factor demand curve downward.

In a coffee processing plant, harvester technology improves such that more coffee is being harvested. This means the plant will need more workers to process the coffee, shifting their factor demand curve upward.

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

In most cases, technological advancements result in an increase in factor demand of a given factor, rather than a decrease.

## 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.

When a paper factory considers hiring an extra employee, they consider the additional cost of adding the employee and the additional benefit of adding the employee. The additional cost of adding the employee is the marginal cost whereas the additional benefit of adding the employee is the marginal benefit.

You should note that most factor markets in the American economy today are characterized by perfect competition. Since there is perfect competition, most buyers and sellers of factors must accept the market prices as they do not possess enough power to force prices. Economists refer to the buyers and sellers in a perfectly competitive market as price takers.

### 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:

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

Marginal revenue product (MRP) refers to the extra revenue generated from adding an extra factor of production.

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.

The calculations are not limited to just labor, in this case, labor is being used, hence, we use "L" for labor.

### 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.

Check out our explanation on Factor Markets to strengthen your understanding of the factor demand curve!

## Factor Demand Curve - Key takeaways

• The factor demand curve is the graphical illustration of the relationship between the price of a factor of production and the quantity demanded of that factor of production.
• The determinants of the factor demand curve are factors that cause the factor demand curve to shift. They include changes in the prices of products, the supply of other factors, and technology.
• Marginal revenue product (MRP) refers to the extra revenue generated from adding an extra factor of production.
• The Wage Rate (W) is the marginal cost of hiring an additional worker.
• The marginal revenue product equals the wage rate.

The factor demand curve is the graphical illustration of the relationship between the price of a factor of production and the quantity demanded of that factor of production.

The labor demand curve and land demand curve are examples of the factor demand curve. You will often come across the labor demand curve since labor is most commonly analyzed.

It is plotted with the factor price on the vertical axis and the quantity demanded of the factor on the horizontal axis.

When there is either:

• a decrease in the price of a product
• a decrease in the supply of other factors
• change in technology that would lead to less of the factor being required

Factor demand refers to the willingness and ability of a firm to purchase factors of production.

## Test your knowledge with multiple choice flashcards

The graphical illustration of the relationship between the price of a factor of production and the quantity demanded of that factor of production:

On the factor demand curve, _____ is on the vertical axis and ______ is on the horizontal axis.

Determinants of the factor demand curve cause ______ in the factor demand curve.

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