Labor Market Equilibrium

Overview In this chapter we want to explore what happens in a competitive labor market. After that we will explore other labor market structures. Plus we will look at applications of these types of labor markets.

Single competitive labor market If the whole economy comprises a single competitive labor market, then the wage and amount of labor employed is determined by the interaction of supply and demand. Then any one firm, or worker, is a wage taker. This means the worker or the firm can not determine the wage alone. Again, the wage is set by the interaction of all parties concerned. Recall from our earlier work that a profit maximizing firm hires labor up to the point where the value of the marginal product is equal to the wage.

Single labor market $ In the market we get W* and E*. Each firm takes W* and hires what they want and when you add that across firms you get E*, which is just the total supplied . S W* D E E*

Equilibrium W* is the equilibrium wage because at this wage both suppliers and demanders obtain the desired amount. At wages higher than W* an equilibrium would not exist because at those wages the quantity supplied is much higher than the quantity demanded – an excess supply. All those willing to supply do not get to trade because there are too few buyers. Since this excess supply will encourage suppliers to change by lowering the wage at which many will work, the initial high wage (relative to the equilibrium) will not last and will change to the equilibrium wage.

More equilibrium At wages lower than W* an equilibrium would not exist because at those wages the quantity supplied is much lower than the quantity demanded – an excess demand. All those demanding do not get to trade because there are too few sellers. Since this excess demand will encourage demanders to change by raising the wage which they will pay for work, the initial low wage (relative to the equilibrium) will not last and will change to the equilibrium wage.

Firms in this environment $ $ W* VMP1 VMP2 E1 E2

Firms in this environment Firms in a competitive market are wage takers and in order to maximize profit they hire labor up to the point where the wage is equal to the value of the marginal product. On the previous slide we see two such firms accept the wage as W*. Each has a slightly different VMP curve but each takes labor until W = VMP. So, for the last worker taken by each firm the VMP is the same. Recall that VMP = output price times marginal product and this concept is telling us about the value of output made by a worker.

Invisible hand The invisible hand concept in economics says that individuals and firms acting in their own self interest achieve something none had even thought or worried about. That something achieved is the greatest value of output for the resources expended. Another way of saying this is that the allocation of resources is efficient. Let’s see how that can be here. Say the firm on the right on screen 5 has to take one more unit of labor and the firm of the left is forced to take one unit less of labor. The total amount of labor used would be the same as before, so we would have the same amount of labor used.

Invisible hand Now the firm on the right would add output but the value of the output would be less than the wage (how do I know this?). The firm of the left would lose output and the value of the output would equal the wage. Thus the value of the output lost is greater than the value of the output gained from the switch and the total value of output must fall from this reallocation of resources. In other words, the original value of output was higher than we could achieve by switching workers to different places. Adam Smith noted this type of result way back in 1776, but he was in England (which really doesn’t matter, but was fun to type).

Efficiency of Competitive Labor Market Equilibrium

Single labor market $ In the market we get W* and E*. Each firm takes W* and hires what they want and when you add that across firms you get E*, which is just the total supplied . S A B C W* D E E*

Single labor market $ S A B C W* D E 1 E*

Producer surplus in the labor market On slide 3 if you focus on the demand curve in the upper left I put a different supply curve and in the market we would have supply and demand equal where there is 1 unit of labor employed. Since the demand is really the value of the marginal product the area of the rectangle from the origin out to an E = 1 and up to the demand is really the value of the marginal product of the first unit. Almost all the area under the demand curve out to E = 1 is the value of the marginal product. So, we just say all the area is the VMP. In the real market outcome with E* the areas A, B and C represent the sum of value of the marginal product for each E out to E*. The areas B and C add up to what the firms pay the labor. So, area A represents revenue labor has helped generate but has not been paid back to labor. It is called the producer surplus and is the profit of the firms if labor is the only input, or it is used by the firms to pay for other inputs and then what is left is profit.

What is producer surplus all about What is producer surplus all about? Well, you see that firms hire labor to help make output. Not only does the labor contribute to revenue that can be used to pay the labor, it pays for other stuff for the firms. This producer surplus is a gain from having trade in the labor market. Worker surplus in the labor market Back on slide 3 if you focus your attention on the lower left of the graph you see I have a different demand with the supply so that only unit of labor is supplied. The rectangle made by the origin out to an E = 1 and up to the supply is a measure of what the supplier would have if they were doing something else and not giving their time here. The rectangle is a little over the supply curve, but we just focus on that part under the supply curve.

Worker surplus If we go all the way out to the equilibrium the area C is a measure of the suppliers’ use of time in some other area instead of supplying labor. The area B + C is what the suppliers earn in the labor market. SO, B is worker surplus and is a measure of what they get over and above what they would get in their next best use. It is a gain from trade in the labor market.

Efficiency In the competitive labor market we see Producer surplus of A Worker surplus of B. These surplus values represent gains from trade. No other amount of labor generates as much gain from trade. In that sense the competitive labor market is said to be efficient.

The law of one wage Before we had one labor market. But, in reality we have many labor markets – perhaps different by geography. On the next slide we show the case of two labor markets and initially we have different wages. In the north the wage is much higher than in the south. Note: we are using perfectly inelastic supply curves to simplify the analysis. This essentially means the worker surplus is the whole area below the wage. If workers are mobile and can freely move to another region we would see folks leave the south and go to the north. The wage will fall in the north and rise in the south. The graphical analysis is shown on the next slide.

Competitive Equilibrium in Two Labor Markets Linked by Migration SS Dollars Employment w* wS DS (b) The Southern Labor Market SN wN DN (a) The Northern Labor Market s A B C Suppose the wage in the northern region (wN) exceeds the wage in the southern region (wS). Southern workers want to move North, shifting the southern supply curve to the left and the northern supply curve to the right. In the end, wages are equated across regions at w*.

Efficiency again As workers leave the south and the wage rises, both producer and worker surplus is lost. But in the north as those workers are added, the wage is lowered and there are additions to both producer and worker surplus. As the wage rises in the south as workers leave the VMP of labor is rising, while in the north the wage is falling and the VMP is falling. But, in the south the workers are leaving low VMP for high VMP in the north. SO, on the net workers are moving to higher valued uses. This is efficient.