Equilibrium Wage

Equilibrium Wages Employment

In a competitive market, equilibrium wages and employment are linked directly. The wage equilibrium in a perfectly competitive economy is the point where the labor demand curve intersects the labor supply curve. According to classical economic theory, if wages are completely flexible, the employment rate will reach its maximum value. Aside from structural unemployment and cyclical unemployment, the flexible wage rate ensures that everyone is employed in society.

The idea behind this assumption of full employment is rather intuitive in theory. The main mechanisms of supply and demand are also valid in the labor market. For example, let's assume that there are two identical workers. One worker is okay with the wage of $15 per hour, and the other worker wants $18 per hour. A firm will choose the first worker before choosing the second. The number of workers that the firm needs to hire depends on its operational needs. If we broaden this example for society, we can grasp the dynamics of the equilibrium wage rate.

In a competitive market structure, the equilibrium wage rate is determined by the constant matchmaking between firms and workers. Nonetheless, according to classical economic theory, laws like minimum wage affect the structure of the labor market, and they create unemployment. Their argument is that if the minimum wage rate is above the equilibrium wage rate in a market, the firms can’t afford the minimum wage, and they will cut positions for workers.

Equilibrium Wages Graph

Graphing equilibrium wages can be beneficial for us since this can help us to realize how the market reacts with respect to different types of pressures.

We show a graph of the labor market equilibrium in Figure 1.

Fig. 1 - The equilibrium wage in the labor market

A few aspects are highly important to grasp here. First of all, as we mentioned before, the equilibrium wage \(W^*\) is equal to the point where the labor supply and the labor demand intersect. This is rather similar to the price of a product in competitive markets. At the end of the day, we can evaluate labor as a commodity. Therefore we can think of the wage as the price of labor.

But what happens when circumstances change? For example, let’s assume that one country decides to open its borders to immigrants. This wave of immigration will shift the labor supply curve to the right due to an increase in people who are now searching for jobs. As a result, the equilibrium wage rate will drop from \(W_1\) to \(W_2\), and the equilibrium quantity of labor will increase from \(L_1\) to \(L_2\).

Fig. 2 - Increased labor supply in the labor market

Now, we can look at another example. Let’s assume that immigration increases the number of business owners. They found new businesses and create new job opportunities. This scenario increases the demand for labor instead of the supply of labor. Since firms need more workers, they will increase the wages to lure workers to their firms. We can show the change in Figure 3. In this scenario, the equilibrium wage rate will increase from \(W_1\) to \(W_2\) while the equilibrium quantity of labor will increase from \(L_1\) to \(L_2\).

Fig. 3 - Increased labor demand in the labor market

Equilibrium Wages Formula

There is no definitive formula for equilibrium wages for global application. Nonetheless, we can set some assumptions and basically some ground rules to refine our knowledge.

Let’s denote labor supply with \(S_L\) and labor demand with \(D_L\). Our first condition is that both labor supply and demand are linear functions with the generic formulas as follows:

\(S_L = \alpha x_s + \beta | \alpha, \beta \in R \land \alpha > 0\)

\(D_L = \delta x_d + \gamma | \delta, \gamma \in R \land \delta < 0 \)

The conditions after the functions basically guarantee the shape of the supply and demand curves. Furthermore, it is reasonable to assume that the demand curve will have a negative slope. In labor markets, lower wage rates will increase the demand for labor since employers can earn more profit. On the other hand, we can expect a similar thing from the supply curve. When the wage rates increase, people will be more willing to offer their labor skills to the market. That is why the supply curve has a positive slope.

Our second assumption is that for an equilibrium wage rate to exist, both supply and demand curves must intersect. We can state the wage and labor rate at this intersection with \(W^*\) and \(L^*\) respectively. Therefore, if equilibrium wages exist, the following conditions should be met:

\(S_L=D_L\)

\(\alpha x_s + \beta = \delta x_d + \gamma \)

The equilibrium quantity of labor \(L^*\) is given by the \(x\) that solves the above equation, and the equilibrium wage rate \(W^*\) is given by the results of either the labor supply or the labor demand curve after plugging in the \(x\).

We can approach the point from another perspective and explain the relationship between the marginal product of labor and market equilibrium. In a perfectly competitive market, the marginal product of labor will be equal to the wage rates. This is highly intuitive since workers will get paid for the amount that they contribute to the production. We can denote the relationship between the marginal product of labor (MPL) and wage rates with the following notation:

\[\dfrac{\partial \text{Produced Quantity}}{\partial\text{Labor}} = \dfrac{\partial Q}{\partial L} = \text{MPL}\]

\[\text{MPL} = W^*\]

Equilibrium Wages Example

We can give an example of equilibrium wages to grasp the concept even better. Let’s say that there exist two functions, one for labor supply and the other one for labor demand in a perfectly competitive factors market.

Imagine that we are observing factors market in a town. Now let’s assume that there exists an equilibrium wage rate of $14 per hour and an equilibrium quantity of labor of 1000 worker hours in this town, as shown in Figure 4 below.

Fig. 4 - An example of the labor market in equilibrium

While keeping their daily lives, townsfolk hear about new job opportunities in a town in the South. Some young members of this community decide to leave the town since they want to earn more money than $14 per hour. After this decrease in the population, the quantity of labor shrinks to 700 worker hours.

While thinking about this situation, employers decide to increase the workers’ wages. This is rather reasonable since the migration has caused a decrease in labor supply in the job market. Employers will increase the workers’ wages to lure workers to their firms. We show this in Figure 5.

Fig. 5 - The job market after a decrease in the supply of labor

Let’s say that after a few seasons, some firms hear words that due to new trade routes in a town in the North, the profits there are much higher. They decide to relocate their firms to the North. After the firms move out of town, the labor demand curve shifts to the left by a significant amount. We show this scenario in Figure 6. The new equilibrium wage is $13 an hour with the equilibrium quantity of labor at 500 worker hours.

Fig. 6 - The job market after a decrease in the number of firms