Some thoughts on the origins of monopsony and minimum wages

For the past couple of weeks, I've been thinking about the problem minimum wages in terms of a game, and I think there is a kernel of good idea here. 

There has been a lot of discussion recently about how unskilled, low wage workers are faced with a job market where the employers have the monopsony power to pay wages below the competitive market rate. Since a monopsony occurs when there is a single payer (the employer) and a large market of sellers (unskilled labor), the employer is able to pay wages below the competitive wage rate.

Let's say that we have two firms in perfect competition producing commodities that are perfect substitutes. For the sake of argument let's say that they are hamburger chains A and B. The cost of their product is a combination of the variable costs of their materials, their labor costs and their fixed costs of operation (building, utilities, etc.). They want to keep their costs to a minimum so that they can compete for a share of the available market. So any thing which causes their costs to rise will mean that they have to raise their prices. But if A raises his prices and B doesn't, then B will take market share away from A. If their fixed costs or the cost of their ingredients increase, then A and B are both affected equally. They both raise their prices by an equivalent amount, and their market shares remain equal. 

Score (0,0).

Now think about the problem of their labor costs. If both A and B Hold their wages steady then neither suffers a loss.

So long as there is a ready supply of low skill labor, there is no pressure for them to raise wages. In fact, there is a downward pressure on their labor costs even under conditions where the wages they pay are below what the labor market would indicate. The reason is that if A raises his wages then B will want to hold his wages. That will allow B to take some share, +a, of the market away from A who loses -a. The risk is obviously symmetric under an exchange of the labels A and B. 

Score (+a,-a).

If labor costs are at or above the market equilibrium, then if both A and B raise their wages they may both suffer a small loss, -b. But that loss is likely to be smaller than if they raise their wages and their competitor doesn't. The risk of the larger loss in the asymmetric wage rise case causes both A and B to keep their wages below the equilibrium. This is possible because there is always a fresh stream of new, unskilled labor. So long as the rapid turnover in their labor supply is small enough that the costs of training are below the costs due to rising wages, it is better for them to Hold wages steady. 

Score (-b,-b).

If both A and B Raise wages and the labor costs are below the market equilibrium, then neither will suffer a loss because the market hasn't changed. In fact, in this situation there could even be a net positive benefit +b to both A and B if they raised their wages because of an increase in the size of the market! 

Score (+b,+b).

Wages are below equilibrium         A B H R H 0,0 -a,+a R +a,-a +b,+b

Wages are above equilibrium         A B H R H 0,0 -a,+a R +a,-a -b,-b

In this case, the monopsony emerges from a sort of Prisoner's Dilemma. Even if they wanted to raise wages, they can't since their competitor can defect and hold their wages, stealing market share. So the monopsony in this situation isn't the result of any sort of collusion or ill will on the part of the employers. They're stuck in a Nash equilibrium that hurts all parties involved.

An increase in the minimum wage provides a way for both companies A and B to increase wages without risking the adverse effects of a competitor defecting and stealing market share.

The idea needs more work, but I think it's on the right track.