Question

The demand for labor by an industry is given by the curve \(L=1200-10 w,\) where \(L\) is the labor demanded per day and \(w\) is the wage rate. The supply curve is given by \(L=20\) w. What is the equilibrium wage rate and quantity of labor hired? What is the economic rent earned by workers?

Short answer

Hence, the equilibrium wage rate is 40; the amount of labor demanded and supplied at equilibrium is 800. The economic rent earned by the workers is 0.

Step-by-step solution

Set the Demand and Supply Equations Equal to Each Other

The equilibrium wage is where the quantity of labor demanded equals the quantity of labor supplied, so set the two equations equal to each other and solve for the wage rate, \(w\), which will yield \(1200-10w=20w\).

Solve for Equilibrium Wage Rate

Moving the second part of the equation on the right hand side to the left hand side to get \( w \) alone: \(1200 = 30w\). Now, divide both sides by 30, which gives \( w = 1200 / 30 \). Thus, \( w = 40 \). So, equilibrium wage rate is 40.

Find Equilibrium Quantity

To find the equilibrium quantity of labor demanded and supplied, substitute \( w = 40 \) into each of the original equations. For the demand equation: \( L = 1200 - 10 * 40 \), and for the supply equation: \( L = 20 * 40 \). Both equations result in \( L = 800 \). So the equilibrium quantity of labor is 800.

Determine Economic Rent

Economic rent is the extra income workers earn above the minimum income they would be willing to accept to do their job, also known as the opportunity cost. Here within given context, the minimum wage workers are willing to accept equals the equilibrium wage rate, which we calculated to be 40. So the economic rent is \(0 (0 = 40 - 40)\)

Key concepts

Labor Demand Curve

The labor demand curve illustrates the relationship between the wage rate and the quantity of labor that employers want to hire. It is typically downward-sloping because, as wages increase, employers tend to hire less labor due to higher costs. In our exercise, the labor demand is represented by the equation \(L = 1200 - 10w\), where \(L\) is the number of workers and \(w\) is the wage rate. This equation implies that for every unit increase in wage, the demand for labor decreases by 10 units.

Understanding how to interpret this curve is essential. When graphed, the x-axis usually represents the quantity of labor, and the y-axis represents the wage rate. As you move down the curve, each point indicates how many workers businesses are willing to hire at various wage levels. This concept is critical in determining the equilibrium wage rate, where the curve intersects with the labor supply curve.

Labor Supply Curve

Conversely, the labor supply curve shows the relationship between the wage rate and the quantity of labor that workers are willing to offer. Generally, this curve is upward-sloping because as the wage rate rises, more people are incentivized to work or workers may offer more hours of their labor. The labor supply equation from our exercise is \(L = 20w\). This equation indicates that for every unit increase in the wage rate, the supply of labor increases by 20 units.

Understanding Labor Participation

As wages increase, not only are existing workers motivated to work more, but individuals who were not previously working may decide to enter the workforce. Therefore, higher wages can attract new participants into the labor market, which is depicted by a movement along the supply curve.

Economic Rent

Economic rent is an important concept in labor economics. It refers to the amount of money workers earn in excess of what they would need to be paid to keep them in their current occupation. In other words, it's the additional income that workers receive that they would not have earned if they worked at their next best alternative. The solution states that in our exercise, since the equilibrium wage rate matches the minimum wage that the workers are willing to accept for their labor, the economic rent is zero.

Opportunity Cost and Rent

The concept of economic rent can also be connected to opportunity costs, which is the value of the next best alternative foregone. When the wages that workers receive match exactly what they would need to accept the job, their opportunity cost and actual wage are equal, leading to an economic rent of zero. This highlights that the industrial labor market is perfectly competitive, with no worker having a special advantage that would garner extra pay.

Quantity of Labor

The term quantity of labor refers to the total number of labor hours that workers are willing to supply or that employers are willing to hire at a given wage rate. In our exercise, this is shown by the equilibrium quantity of labor, which was found to be 800 when the wage rate is set at 40. This figure is the point at which the labor demand curve intersects the labor supply curve, indicating that both employers and employees are satisfied with the wage rate and quantity of labor.

Equilibrium in the Labor Market

At this equilibrium point, the market clears, meaning that all the labor supply is employed with no surplus or shortage in the labor market. It is essential to understand that the quantity of labor is not fixed and can be influenced by various factors such as changes in the economy, technology, education, and government policies, which can shift the supply and demand curves and as a result, the equilibrium wage rate and quantity of labor.