Markets for Factors of Production in Economics

Jason Moore

These are my notes on markets for factors of production.

The three main factors of production are labor, physical capital, and land. Firms derive the demand for labor by determining the value of marginal product of labor. The supply of labor is determined by trading off the marginal benefit from labor given earnings against the marginal cost, the value of forgone leisure.

 

Wage inequality can be attributed to differences in human capital, differences in compensating wages, and discrimination in the job market. In addition to labor, a producer must derive the demand for physical capital and land to achieve its production objectives. 

 

The market for labor is of particular importance in the economy because it affects all of us. The market for labor is composed of suppliers and demanders. Workers produce goods and services and therefore are known as factors of production. Remember that a factor of production is used in the production of other goods.

 

Markets for factors of production are somewhat different from markets for goods and services that we consume, because the demand for factors of production is delivered from the demand for final goods and services. 

 

Although firms tend to use many factors of production, the main factors that we will focus on are labor, machines, and land.

 

In the market for labor, the roles of demander and supplier are reversed: businesses are buyers of labor and individual workers are suppliers of labor.

 

All firms rely on labor as a major factor of production. Workers operate machines and often perform tasks more efficiently than machines. 

 

The law of diminishing returns states that the marginal productivity of an additional unit of labor eventually decreases as we increase the number of workers. 

 

The value of marginal product of labor is the contribution of an additional worker to a firm’s revenues. 

 

We have now seen two ways to maximize profits.

  1. Choose the total quantity of production in order to maximize profits, so expand production until marginal cost=price
  2. Optimally choosing its labor by expanding its workforce until the marginal product of labor * price = vmpl=wage

 

To construct the market supply curve, we need to aggregate the individual labor supply curves. To do this, we horizontally sum the individual labor supply curves. 

 

The substitution effect implies that when the price of leisure increases, people will substitute working for relaxing. 

 

There are several key determinants of where the labor demand curve will be situated. Two important factors are:

  1. Price of the good that the firm is producing
  2. Technology of the firm

A labor saving technology is a type of technology that substitutes for existing labor inputs, reducing the marginal product of labor. Labor-complementary technologies are those that complement existing labor inputs, increasing the marginal product of labor.

 

Shifts in labor supply also affect equilibrium wage and employment levels. We discuss three main factors that shift labor supply:

  1. Population changes
  2. Changes in worker preferences and tastes
  3. Opportunity costs

There are three important features of the labor market that may give rise to differences in wages across workers:

  1. Differences in human capital
  2. Differences in compensating wages
  3. Discrimination in the job market

 

One explanation for the wage difference is that people have very different levels of skills and therefore different levels of productivity. Economists refer to each person’s stock of skills for producing output or economic value as human capital. Differences in human capital result in differences in wages.

 

The wage differences that are used to attract workers to otherwise undesirable occupations are known as compensating wage differentials. Wage differentials based on risk and unpleasantness are important factors to consider when examining wage differences across jobs, but there are also reasons we may see workers in the same job getting paid differently. 

 

A third major factor in determining wages in the labor market is the nature and extent of discrimination that is present. Economists have pinpointed two major theories for why employers might discriminate, taste-based and statistical discrimination. 

 

Taste-based discrimination occurs when people’s preferences cause them to discriminate against a certain group. It is important to note that wages can be different between groups not only because an employer has a taste for discrimination but also because of other factors like human capital. 

 

Statistical discrimination occurs when employers use an observable variable to help determine whether the person will be a good employee. 

 

Technology can be either labor saving or labor complementary. It can also be skill saving or skill complementary. Skill biased technological changes increase the productivity of skilled workers relative to that of unskilled workers. The primary technological change over this time period has been advances in computing power. 

 

Despite our focus so far on labor as an input to production, there are other factors equally important to the production process. 

 

Recall that the value to a firm of adding each consecutive unit of labor is given by multiplying the output price and the marginal product of labor.

 

Physical capital is any good, including machines and buildings, used for production. A firm will expand its physical capital until it is not worthwhile to do so. The value of marginal product of physical capital is the contribution of an additional unit of physical capital to a firm’s revenues.

 

The same is true for uses of land. Land includes the solid surface of the earth where structures are built and natural resources. 

 

Although the economic framework for deciding how much of the three inputs to use is identical, labor has one major difference from physical capital and land: both physical capital and land can be either rented or owned, whereas labor cannot be owned. When rented, the firm must pay the rental price of physical capital, and to use land it must pay the rental price of land. By rental price, we mean the price of using a good for a specific period of time. 

 

Producers determine the optimal mix of labor, physical capital, and land when making production decisions. Markets for these factors of production operate in much the same way that markets for final goods and services function. Firms expand their use until marginal benefits equal marginal costs. Determining the demand for labor centers on the concept of the value of marginal product of labor, which is the contribution an additional worker makes to the firm’s revenues.

 

When making decisions on how to spend our time, we face opportunity costs. There is a trade-off between labor, which comprises activities that earn money, and leisure, which is time spent on activities other than earning money. The opportunity cost for one hour of leisure is the income that we would have earned by working for that one hour.

 

Large wage differences exist across people and jobs. The differences stem from three main sources: human capital differences, compensating wage differentials, and discrimination. As with labor, firms expand their use of physical capital until the value of the marginal product equals the price of physical capital, and they likewise use land until the value of the marginal product of land equals the price of land. 



Suppose that at your firm the relationship between output produced and the number of workers you hire is as in the following table.

  1. Marginal product = 18, 14, 10, 9, 5, 4

 

Is the relationship between output and labor consistent with the law of diminishing returns?

  1. Yes, the marginal product declines as successive units of labor are hired

 

Suppose your firm is a perfect competitor in the output market and the labor market.

If the price of output is $7 and the wage rate is $28, your firm should hire:

  1. 6 workers

If the price output falls to $2 and the wage remains $28, your firm should hire:

  1. 2 workers

 

Consider a businessman that owns three different coffee shops with production functions shown below. Fill in the blanks.

1 100 100 20 20 40 40

2 130 30 40 20 70 30

3 140 10 60 20 100 30

4 140 0 80 20 110 10

 

Suppose there are 8 workers available and the businessman’s goal is to maximize total coffee production.

Using this information, he should assign:

  1. 2 workers to arabica alley
  2. 3 workers to barista bar
  3. 3 workers to coffee cafe
  4. Total production will be 290 cups

Suppose the businessman believes in letting the labor market help in achieving optimal outcomes. Again, there are 8 eager workers.

The equilibrium wage he will set would be:

  1. $20

At this wage the total production of coffee would:

  1. Equal to the amount you found in the previous question

 

You run a factory that uses pottery wheels to make pots. You can hire anywhere between 1 and 3 skilled artisans, and you can rent 1 or 2 pottery wheels. Pots sell for 100 each. The total production of your factory is shown in the following table.

Workers

1 2 3

Machines 1 10 13 15

2 12 16 19

 

Suppose you rent one machine and hire one worker.

You would be willing to pay:

  1. 300 to hire a second worker. Consider the value of the marginal product of labor

Suppose you rent one machine and hire one worker

You would be willing to pay a rental rate up to:

  1. 200 to acquire a 2nd machine

Suppose the wage is 275. If you have one pottery wheel,. The number of workers you would want to hire is:

  1. 2

Pottery wheels are:

  1. Labor complementary

 

A production function shows:

  1. The number of workers employed and the corresponding output levels that will be produced

According to the law of diminishing returns:

  1. The marginal productivity of an additional unit of labor eventually decreases as the quantity of labor increases

Using the 3 point curved line tool, add a production function to the graph

  1. Start the line at 0,0 and gently slope upwards until it covers most of worker numbers



The value of marginal product of labor is:

  1. A and C.
  2. Given by the marginal product of labor times the price of the firm’s output
  3. The contribution of an additional worker to a firm’s revenues

Complete the following table. Assume that the selling price of the firm’s output is 5 per unit

Workers employed Marginal Product VMPL

1 24 120

2 20 100

3 16 80

4 12 60

5 8 40

 

When the firm’s VMPL is plotted in a diagram with the quantity of labor measured along the horizontal axis, the resulting curve will be:

When plotted, the vmpl is a downward sloping curve, which is the firm’s demand curve for labor

  1. Downward sloping and demand curve for labor

 

The following table gives the value of marginal product of labor for a competitive firm.

Workers VMPL

1 180

2 150

3 120

4 90

5 60

6 30

 

Because this firm is competitive and haS NO CONTROL OVER ITS PRODUCTS’S PRICE, THE DECLINING VALUES FOR VMPL ARE A RESULT OF DIMINISHING:

  1. Marginal productivity

When the vmpl is plotted in a diagram with the number of workers measured along the horizontal axis, the resulting curve is the firm’s:

  1. Demand for labor

Draw the firm’s demand for labor curve

  1. Draw a downward sloping demand curve
  2. Draw a horizontal line at 90 dollars

According to the diagram, the profit maximizing level of employment for this firm is:

  1. 4 workers

 

How does the labor-leisure trade-off determine the supply of labor?

  1. An increase in the wage rate is an increase in the opportunity cost of leisure, and can therefore be expected to reduce the amount of leisure one wishes to consume. Choosing less leisure is equivalent to supplying more labor, thus yielding a positive relationship between the wage rate and the amount of labor supplied

 

How do labor saving technologies differ from labor complementary technologies:

  1. All of the above
  2. Labor-saving technologies substitute for existing labor inputs, while labor-complementary technologies augment existing labor inputs
  3. Labor-saving technologies decrease the marginal product of labor, while labor-complementary technologies increase the marginal product of labor
  4. Labor-saving technologies result in lower wages and less employment, while labor-complementary technologies result in higher wages and more employment

 

Complete the following table by identifying the two types of technological change

Gps location devices in delivery trucks:

  1. Labor-complementary technology

Radio frequency identification tags in grocery stores

  1. Labor-saving technology

 

For a long time, your firm has been paying its workers a wage of 20 per hour and your employees have been happy to work 40 hours per week at this wage. Business is suddenly booming and your firm would really like your workers to agree to a 50 hour work week in order to meet this new demand for your product. You are considering two strategies:

You would raise the wage for all hours worked from 20 to 22 per hour

You would leave the wage for the first 40 hours per week at 20 but offer 30 per hour for hours worked above 40 hours.

Both strategies have the same cost of 1100 if a worker chooses to work 50 hours.

Which strategy is more likely to lead your employees to agree to a 50 hour work week?

  1. Strategy 2, because the marginal cost of not working increases significantly after 40 hours of work

 

The patient protection and affordable care act requires all employers with at least 50 full time equivalent workers to offer health insurance to their full time employees or pay a fine of up to 2000 per employee. Some people have argued that ACA will lower employment. This problem looks at an important issue in this debate.

Suppose the government passes a law that requires firms to offer health insurance to their workers. The cost of the insurance is equal to 2 for each hour an employee works.

How will this law affect firms’ demand for labor?

  1. Demand for labor will shift down by 2

Suppose workers consider two dollars of health insurance paid by firms to be the equivalent of 2 in wages. How will this law affect the supply curve of labor?

  1. Supply of labor will shift down by 2

Consider an industry where the equilibrium wage is 15 per hour and 100 workers are employed.

How will this law affect the equilibrium quantity of labor in this labor market?

How will it affect the equilibrium wage in this industry?

  1. D2 = below D1
  2. S2 = below S1

According to your graph, the equilibrium wage:

  1. Falls

The equilibrium quantity:

  1. Stays the same

Now suppose workers consider a dollar of health insurance paid by firms to be worth less than 2 in wages.

How will this law affect the equilibrium quantity of labor in this labor market?

How will it affect the equilibrium wage in this industry?

  1. The equilibrium wage and quantity both decline, with the wage declining less than in the previous case where workers consider the insurance to be the equivalent of 2 in wages

 

The figure on the right shows the market for labor in a given industry.

The demand curve is downward-sloping because marginal productivity:

  1. Falls, as more workers are employed

While the supply curve is upward-sloping since an increase in the wage increases the opportunity cost of:

  1. Leisure

Now suppose that the price of the product being produced increases, all else constant.

Using the line drawing tool, show the impact of this event.

Note that a price change does not impact the supply curve

  1. Demand curve with higher equilibrium price

According to the graph, the consequence of the change in price is a:

  1. Higher market wage
  2. Higher level of employment

 

Technologies that substitute for existing labor inputs are known as:

  1. Labor-saving technologies

With this type of technological change, the marginal productivity of existing labor inputs will:

  1. Decrease

Using the line drawing tool, show the impact of this new technology

  1. Draw demand curve with lower equilibrium point

The consequence for workers will be a wage rate that is:

  1. Lower

Hours of employment that are:

  1. Lower

 

Occurs when people’s preferences cause them to discriminate against a certain group:

  1. Taste-based discrimination

Occurs when expectations cause people to discriminate against a certain group

  1. Statistical discrimination

The owner of a company that manufactures  automobile parts states that it will not hire gay or lesbian employees. This is an example of:

  1. Taste-based discrimination

 

Which of the following is not an important determinant of wage inequality within an economy?

  1. Differences in connections to influential people

Human capital is the:

  1. A db B
  2. Experience that people derive from spending more time on a job
  3. Skills and knowledge that people obtain by furthering their schooling

Compensating wages are the wage premiums:

  1. Paid to attract workers to occupations to otherwise undesirable jobs



When it comes to determining the appropriate quantity of physical capital to use, the firm employs a decision rule that is conceptually:

  1. Identical to, the approach it takes in choosing the number of workers to hire

A firm will employ physical capital until:

  1. The value of marginal product of capital equals the rental price of capital

The following table gives the value of marginal product of capital for a competitive firm

Machines VMPK

1 120

2 100

3 80

4 60

5 40

6 20

If the rental price of capital is 80 per machine, this firm will employ:

  1. 3 machines

Two major theories for why employers might discriminate are:

  1. Taste based and statistical discrimination

Suppose an employer avoids hiring youthful workers because she worries that their skill level makes them unproductive. In this case, the employer is practicing:

  1. Statistical discrimination

If an employer’s discrimination signals that she is willing to forego profits, the she is engaging in:

  1. Taste based discrimination

 

A production function shows:

  1. The number of workers employed and the corresponding output levels that will be produced

According to the law of diminishing returns:

  1. The marginal productivity of an additional unit of labor eventually decreases as the quantity of labor increases

 

The figure on the right shows the market for labor in a given industry.

The demand curve slopes downward because:

  1. Marginal productivity falls as more workers are employed

The supply curve slopes upward since the opportunity cost of leisure:

  1. Rises following an increase in the wage

Using the line drawing tool, show the impact of this event.

  1. Draw supply curve to left of equilibrium supply

According to the graph, the consequence of the change in attitudes is a:

  1. Higher market wage and a lower level of employment

 

Suppose you decide to start a business printing t-shirts. The table below summarizes the number of machines you will need to print t-shirts for a given level of output as well as the marginal product of each additional machine. Assume the equilibrium price of t-shirts is 7.

Calculate the value of marginal product of capital.

Output Machines Marginal product VMPK

60 1 60 420

135 2 75 525

217 3 82 574

290 4 73 511

358 5 68 476

 

If the rental price of capital is 511 permachine, you will employ:

  1. 4 machines

 

You should also read: