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 \(L=20\) tw. What is the equilibrium wage rate and quantity of labor hired? What is the economic rent earned by workers?

Short answer

The equilibrium wage rate is $40 and the number of labor hired is 800 units. The economic rent earned by workers is $40.

Step-by-step solution

Solving for equilibrium wage rate and quantity

Setting the labor demand and supply equal, we get to \(1200-10w = 20w\). Solving this equation gives \(w = 40\), and substituting \(w = 40\) into either the labor supply or demand equation, we get \(L = 800\). So, the equilibrium wage is $40 and the equilibrium quantity of labor is 800 units.

Calculating economic rent

To calculate the economic rent, we can solve the supply curve for \(w\) when \(L=0\). Doing so gives \(w = 0\), which suggests that the minimum wage workers would accept for this job is $0. We then subtract this from the equilibrium wage (\(40 - 0 = 40\)), hence the economic rent (the additional amount that workers receive because the equilibrium wage rate is more than the minimum they would accept) they earn is $40.

Key concepts

Labor Demand

Understanding the labor demand is crucial in grasping how the job market operates. In economic terms, labor demand refers to the number of workers that employers are willing and able to hire at a given wage rate, within a specific time period. It's represented graphically by a demand curve, which typically slopes downwards. This reflects the inverse relationship between the wage rate and the quantity of labor demanded; as wages increase, employers are less inclined to hire additional workers because of the higher cost.

In our exercise, the labor demand curve is given by the equation \(L = 1200 - 10w\), where \(L\) is the labor demanded and \(w\) is the wage rate. Economically, this equation implies that for every one dollar increase in wages, the quantity of labor demanded decreases by 10 units. This relationship is fundamental in finding the equilibrium in the labor market.

Wage Rate

The wage rate is the price of labor; it represents how much workers are compensated for their work per unit of time, like an hour or a day. Wage determination involves several factors, including educational qualifications, skills, experience level, and the amount of labor available. The wage rate plays a pivotal role in both the supply and demand for labor. Workers supply labor in exchange for wages, and employers demand labor based on the wage rate they must pay.

In the context of our exercise, the equilibrium wage rate is the particular rate at which the quantity of labor demanded by the industry equals the quantity of labor supplied by workers. We found this rate to be \(40, which means that at \)40, workers are willing to supply the same amount of labor hours that employers want to purchase.

Economic Rent

Economic rent is a term used in economics to describe the amount of money earned that exceeds what is economically or socially necessary. This can occur in any market, but for labor, it refers to the difference between what workers actually get paid and the least amount they would be willing to accept for their work – also known as the reservation wage. Economic rent arises due to market conditions, such as a shortage of a particular type of labor, which elevates the wage rate above the equilibrium level.

According to our exercise solution, the economic rent earned by the workers is \(40. Given that the minimum wage workers would accept for this job is hypothetically \)0, the entire equilibrium wage rate is seen as economic rent. However, in reality, workers would have some minimum positive wage below which they would not supply labor, and the economic rent would be the equilibrium wage minus this minimum wage.

Equilibrium Quantity of Labor

The equilibrium quantity of labor is the quantity at which the labor demand curve intersects with the labor supply curve. It reflects a state of balance in which the quantity of labor that employers want to hire aligns exactly with the quantity that workers are willing to supply at a particular wage rate. No excess labor supply (unemployment) or excess labor demand (vacancies) exists at this point.

In our textbook problem, after setting the labor demand equation equal to the labor supply equation, we established that the equilibrium quantity of labor is 800 units. This is the amount of labor the market will support at the equilibrium wage rate of $40. It represents a harmonization of employers' desires and workers' needs in the labor market, providing a snapshot of market efficiency at this particular wage rate.