Sunday, February 24, 2013

Monopsony and the Minimum Wage

A monopsony is a market is characterized by many sellers and a single buyer.    The traditional microeconomic analysis of a monopsony is a bit of a mirror image of a monopoly.  

A monopolist faces the "industry" demand curve.   Marginal revenue is less than price for any quantity the monopolist might produce.   Because of the law of demand, to sell another unit of output requires a lower price.   That price is additional revenue for the firm.   However, lowering the price implies that less is earned on all of the output that could have been sold if the price hadn't been cut.  The decrease in revenue from the other units must be subtracted from the price to get marginal revenue--the additional revenue earned from producing and selling and additional unit of output.

Profit is maximized  at a level of output were marginal revenue is equal to marginal cost.   For this to be a maximum profit, the monopolist must then charge what the market will bear, a price greater than marginal cost.   This is at a level of output less than where price equals marginal cost.   The monopolist's price is "too high" and production is "too low" compared to perfect competition.   

Perfect competition can involve all sorts of assumptions (some wildly implausible,) but the key one in this context is that the typical firm takes the current market price as independent of it particular level of production.   This makes marginal revenue equal to price, and so the profit maximum is where price equals marginal cost.   This exhausts all gains from trade from producing the product.  

A monopsonist faces the "industry" supply curve.   The traditional analysis assumes that the law of supply applies to whatever the monopsonist is buying.   Suppose the monopsonist is purchasing some resource that will be used to produce a product for sale.   The marginal cost of the resource is greater than the price the monoposonist pays.    The law of supply implies that the monopsonist must offer to pay more to purchase another unit of the resource.   The amount paid for that unit is a cost to the monopsonist, but the extra amount paid for all of the other units that could have been bought if the monopsonist hadn't offered to pay more is also a cost.   Together, those represent the marginal cost for the monopsonist, which is greater than price (except for the very first unit.)

The monopsonist maximizes profit by purchasing an amount of the resource where the marginal cost of the resource is equal to marginal revenue product of the resource.   The marginal revenue product of the resource the additional revenue that can be earned by selling the additional product that can be produced with an additional unit of the resource.   For this to be a profit maximum, the monopsonist must pay no more for the resource than he must, which is less than the marginal cost.    The amount paid for the resource is less than the marginal revenue product.   The amount paid for the resource is "too little" and the amount of the resource purchased and utilized in production is "too little" compared to perfect competition.

Perfect competition in this context would require that the typical firm takes the amount that must be paid for a resource as independent of the amount it purchases.   This makes the marginal cost of purchasing the resource equal to the price that must be paid.  The profit maximum would be where that the price of the resource is equal to the marginal revenue product.   This would exhaust all gains from trade.

How does this relate to labor?   Suppose there is a isolated mountain valley.    Some families farm steep and rocky hillsides.   Some have nice bottom land.   The productivity of the each families' land varies.    One lucky hillside farmer discovers a rich vein of coal on his land.   He opens a coal mine and hires his neighbors to work for him mining the coal.   If the coal company offers a low wage, then only the farmers with the worst land will abandon their farms and come to work in the mine.   If it offers a higher wage, more farmers, with slightly more productive land, will give up farming for a life in the mines.    If it pays enough, even those families with the fine bottom land will decide that farming corn isn't worth it, and go into the mines and dig coal too.  

The coal company faces an upwardly sloping supply curve for labor.   If it hires another miner, more coal will be dug and it can be sold generating additional revenue.   The marginal revenue product of labor is the added revenue that can be earned from the extra coal that can be dug by the additional miner.

But to get another farmer to abandon his farm and go into the mine, the coal company must raise the rate of pay.    The wage  the coal company pays that additional miner is a cost, but the extra amount paid to all of the other miners who found the lower wage better than their rocky hillside farms must be included as well.   The wages earned by the added miner, plus the added wages paid to all of those already working in the mine is the marginal cost of labor.

The profit maximum for the coal company is where the marginal cost of labor is equal to the marginal revenue product of labor.     The wage paid to the "marginal" worker plus the added wages paid to all of the other workers already in the mine must equal the extra revenue obtained from selling the extra coal dug by that marginal miner.   The wage paid to that marginal miner is just a bit more than what he could have earned if he stayed on his farm, and it is less than the marginal revenue product of labor, the amount of revenue generated by the coal he can dig.

Consider a farmer who makes just enough money on his farm that going into the mine is not worth it.     He is growing corn and selling it.    If he went into the mine, that corn would not be grown.  That output would be sacrificed.   But he would dig some coal, which the coal company would sell.   Because the marginal revenue product of labor in the coal mine is greater than the wage, it is very possible that the extra coal that could be produced is worth more than the corn that would be sacrificed.     There are gains from trade available.  

The coal company can earn enough more from the coal to more than compensate  the farmer for what he does not earn from the corn he could not grow.   They should be able to make a mutually beneficial exchange.   The "problem," is that if the coal company pays this marginal farmer more, it must pay all of its other miners more as well.   It is the extra amount it must pay them that makes it too costly to hire the additional miner.

Suppose the monopsony breaks down.   All the miners discover than they can easily move to the city and earn a bit more than what that marginal farmer required before he would give up farming.   The coal mine must raise all the miners pay to keep them from moving to the city.   And since it has to pay more than what that marginal farmer required anyway, it hires him.  Now, the "going wage" depends on what they are paying in the city.    There is no longer a monopsony, and the coal company hires the amount of miners such that the marginal revenue product of labor is equal to that given wage.   If that wage is anywhere between what the monopsonist was paying and the marginal revenue product of the amount of labor he was using, then he will pay more and hire more.

Suppose instead that the coal company suddenly has a flood of applications from outsiders seeking employment at the wage that was being paid.   There is no longer a monposony, and the coal company will hire these outsiders until the marginal revenue product of labor equals the current wage. 

This suggests that there is, in a sense, a shortage of labor at the current wage.   If large numbers of workers were too appear willing to work at the current wage offered by the monopsonist, he would hire them.  

A minimum wage mimics the impact of the breakdown of the monopsony.   If a minimum wage is fixed anywhere between the wage the coal company is paying and the marginal revenue product of labor, then the coal company will both pay more and hire more labor.   If the minimum wage were set at the wage where the marginal revenue product of the coal equals what the marginal farmer must be paid to give up farming, which is really the marginal revenue product of the corn they don't grow, then the wage will equal the marginal revenue product of labor and coal employment will be maximized.  Or more exactly, the allocation of labor between corn farming and coal mining will be optimized.  The result would be similar to perfect competition in the labor market.

The fundamental problem with this analysis is that the dilemma faced by the coal company is that to share in the gains from trade from hiring one more worker, it must pay extra to all the other workers too.

But why would the coal company pay the other workers anything more?   The entire "problem" comes from assuming that all workers are paid an identical wage.   That one wage paid to all workers must be increased to attract the marginal worker.

 In a competitive labor market, something like this is true.    If a firm wants to hire more, it may have to pay more.   But that will make other firms pay more too.   And if a firm doesn't pay all of its current workers more, it will lose some of them to other firms.  

But the whole point of the monopsony argument is that the labor market is not competitive.    If the coal mine paid the marginal farmer more than its current workers so that he comes into the mine as well, it is called wage discrimination.     By negotiating separate wage agreements for each miner, the coal mine can obtain an amount of labor so that the marginal revenue product of labor equals the marginal revenue product of the sacrificed corn.   Those farmers that would not have been hired under the uniform wage policy can be paid a differentially higher wage.

Unfortunately for workers, the logic of wage discrimination is that each worker is be paid a different wage, only slightly higher than his opportunity cost.   The wage for each and every miner would be only slightly than what he could have earned by staying on the farm.   This is called perfect wage discrimination.

Just as monopsony is a sort of mirror image of monopoly, wage discrimination is a mirror image of price discimination.    For example, a drug company charges a high price for medication in the U.S., but a low price in Africa.    The difficulty is that there is an incentive for resale.   Purchasing the drugs at a low price in Africa and then reselling in the U.S. results in arbitrage profits.    Perfect price discrimination is the rather impractical policy of charging each and every buyer the most he or she is willing to pay, and somehow preventing resale.  

In the labor markets, resale isn't a problem.   If a monoponist were buying corn for a low price in a region with low costs and paying a higher price in a region with higher costs, then arbitargeurs would by up corn in the region where the monopsonist is paying the low price and sell it to the monopsonist in the high cost region where he pays the high price.    (On the other hand, the coal company in my example would need to worry about some existing miners quitting and instead growing corn on the farm just abandoned by the marginal farmer.   Pretty ugly--I will hire you to mine coal at wage higher than the rest of the workers, but only if you promise to leave your farm idle.)

With perfect wage discrimation, or just sufficient wage discrimation to exhaust all the gains from trade, a minimum wage will not increase employment.   On the other hand, as long as it is no higher than the marginal revenue product of labor, it would raise the wages of all of the workers being paid wages less than the marginal revenue product of labor without there being any decrease in employment.

In reality, there are many firms that expand and hire more workers.  The practice of paying the new workers more than the existing workers probably exists, but doesn't seem common.   Usually, new workers are paid less than existing workers.   On the other hand, firms wanting to expand and facing an upward sloping supply curve for entry level workers might raise starting pay relative to what it was before without also increasing the wages of all current workers.   That is, a firm with a monopsony might cause wage compression.    This doesn't leave much room for higher minimum wages to increase increase employment or raise the wages of substantial numbers of existing workers without reducing employment.   The existing workers already make more than potential entry level workers.

My vision of the real world is that it is rife with monopoly, monopsony, and all sorts of price and wage discrimination.   But,  this is in the context of lots of compeition.   Competition is "imperfect," but  the gains and losses in efficiency are small and fleeting in  world of creative destruction.

Still, I wouldn't be surprised if the monopsony effect resulted in some firms hiring more workers due to a higher minimum wage.   Unfortunately, that same increase in the minimum wage will push the wage above the marginal revenue product of labor for other firms so that they hire fewer workers.   

The notion that government operates like an omniscient benevolent despot and could and would set a wage in each and every market so that competitive equilibrium is approximated is completely unrealistic.     I think a more plausible starting place would be politicians trading off the loss of employment versus the increase in wage income.   That would suggest that minimum wages would be set above the marginal revenue product of the current level of employment.   Of course, reduced profits to firms, very significant politically relevant short run, and higher prices to those purchasing the products might relevant.  

During the Bush administration, the increase in the minimum wage was combined with tax benefits for small business.   I am sure that was all based upon finding a wage rate that would cause employment to expand in monopsonistic markets to approximate the competitive equilibrium.  Right.

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