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Labor Demand

Labor Demand and Finding Equilibrium

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Labor Demand

The firms who sold goods and services in the unit on supply and demand now become the buyers in the labor market. Firms need workers to make products, design those products, package them, sell them, advertise for them, ship them, and distribute them, among other tasks. No worker will do this for free, and so firms must enter into the labor market and buy labor. Firms determine the amount of labor that they demand according to several considerations: how much the labor will cost (as represented by the market wage), and how much they feel they need, much in the way that buyers in the goods and services market buy according to the market price and their own needs.

Marginal Revenue Product

Firms are willing to buy labor up to the point where the marginal revenue product of labor is equal to the market wage. What does this mean? The marginal revenue product is the extra revenue a firm generates when they buy one more unit of input (in this case, the input is labor: a unit of labor isn't a new employee, it's another unit of work; an example would be an additional hour of work). As long as the income generated by extra hours of work balances (or exceeds) the wages paid for those extra hours of work, firms will be willing to pay for more labor.

If the marginal revenue product (MRP) of labor is equal to the market wage, the firms will be at their optimal point of labor consumption, since buying more labor would mean that the MRP is less than the wage, and buying less labor would mean that the MRP is greater than the wage. If the marginal revenue product of labor is less than the market wage, then the firms are using too much labor, and those firms will probably cut back on the hours they buy until the MRP of labor is equal to the wage.

MRP > w : The firm will buy more labor
MRP = w : The firm is buying the right amount of labor
MRP < w : The firm is buying too much labor

Law of Diminishing of Returns

Why is this the case, that labor demand is at its optimal point when MRP of labor is equal to the wage? This holds true because of the law of diminishing returns. When a firm is hiring workers and deciding how many hours of labor it needs, it operates with the knowledge that the first hour added will make the biggest difference. For a while, every additional hour of labor for which a firm pays will yield a large marginal revenue. However, as the workers put in more and more time, each additional hour of work will yield less revenue. This phenomenon is true for several reasons: as the workers make more and more products, there may be a surplus, and not enough demand for the goods, in which case the marginal revenue would eventually fall to 0. Another reason underlying this fall in production is that after a certain point, extra workers and extra hours can be unproductive.

Imagine, for instance, that a small furniture store is hiring workers. One worker will get a good deal done on his own. The second worker will probably be productive, as well. The sixteenth worker, however, would probably get nothing done, since there wouldn't be enough space or tools to make furniture. Between the second and the sixteenth worker, we would see a gradual drop in marginal productivity, a trend we call the Law of Diminishing Returns: additional workers may add to productivity, but each worker contributes less, until the marginal product (MP) is 0.

Figure %: Diminishing Returns in the MRP of Labor

Because firms will logically hire a new worker or pay for extra hours only as long as these actions will yield a net profit (MRP > w), we can assume that their demand curve is going to be the same as the curve representing the MRP of labor. This is because, as the MRP of labor falls, firms will hire less additional labor. When the MRP is high, they will try to hire more workers for more hours. Thus, we can use the MRP of labor curve to approximate a firm's labor demand. The intersection of MRP with the wage determines how much labor a firm is willing to hire:

Figure %: Labor Demand Curve
In this case, when the wage is set to w, the furniture store will want thirteen units of work (in this case, workers). The fourteenth worker would not generate enough revenue to cover his wages, and the twelfth worker more than covers his wages. The thirteenth worker exactly covers his wages with his MRP, so the store can be sure that they are getting the maximum amount of revenue out of their optimized hiring decision.

Figure %: Labor Demand Curve

Aggregate Demand Curve for Labor

Just as we added all individual demand curves to find aggregate demand in the goods and services market, we use horizontal addition to add together all individual demand curves for labor to find the aggregate demand for labor. If you have equations representing different labor demand curves, simply add them together to find the new, aggregate demand. Graphically, add the quantities demanded at each wage level to generate a new labor demand curve. You can see how this is done in the Supply and Demand SparkNote.

Equilibrium in Labor Markets

Once you have generated aggregate supply and demand curves for labor, finding the market equilibrium, as with the goods and services market, is simply a matter of finding the intersection of the two curves (unless there is an artificial restriction on the market, such as a minimum wage). Let us consider two cases: an unrestricted labor market with shifts in the supply or demand curves, and a restricted market with a minimum wage.

Unrestricted Labor Market

First, let us consider the market for hot chocolate when the price of marshmallows increases. Assuming that marshmallows and hot chocolate are complementary goods, the rise in the price of marshmallows causes a drop in the demand for hot chocolate. When demand for hot chocolate shifts in (drops), the price of hot chocolate falls. This drop in the price of hot chocolate lowers the MRP of every worker in the hot chocolate industry.

Why is this the case? Say that Charlie the hot chocolate maker can make 1000 packets of hot chocolate every day. If the price was originally $1 a packet, his MRP was $1000 a day. If the price falls to $0.75 a packet, Charlie can still only make 1000 packets a day, and so his MRP has fallen to $750. MRP, remember, is equal to the price times the marginal product of each worker.

MRP = (P) x (MP)
Figure %: Drop in MRP of Labor
Therefore, when because of the drop in price the MRP shifts in across the board, firms, meaning Charlie, will decide to hire fewer workers (or ask for fewer hours of work), since their optimal point of labor consumption has shifted inwards.
Figure %: Drop in Labor Demand
Since the drop in MRP of labor will affect all firms in the hot chocolate industry, this will affect the aggregate labor demand curve, as well, shifting it inwards. Assuming that there is no change in labor supply, the net effect is that the wage paid to hot chocolate workers will drop:
Figure %: Drop in Wage
In reality, it is unlikely that a drop in the price of marshmallows would have such a drastic effect on the hot chocolate industry. While there may be some effect, it won't be as severe as the one seen in the graphs above. This is because the workers in the hot chocolate industry may be able to find higher paying jobs in other industries, making shoes or hairbrushes or tie racks. This would cause an inwards shift of the labor supply curve, which would further decrease the quantity of labor used in the hot chocolate industry, and would also have the effect of raising wages paid to hot chocolate workers.
Figure %: Shift in Labor Supply
The green equilibrium point will be an intermediate equilibrium if these change are not simultaneous (that is, if the demand curve shifts first, and after a time lapse, the supply curve then shifts). If the two changes are simultaneous, then the equilibrium will shift directly from the first to the final point.

Restricted Labor Markets

What happens when the labor market is restricted in some way? Recall the case in the goods and services market where the government installs artificial limits on the market, such as taxes, price ceilings, or price floors. The government does similar things in the labor market, as well. Workers pay income taxes on their wages, and firms are required to pay no less than a regulated minimum wage for the labor they demand. These restrictions cause distortions in the way that the labor market works.

For instance, the U.S. runs on a progressive income tax system: for the first chunk of money you make, you pay no taxes, so you get to take home every penny that you earn. For the second chunk of money, you pay some taxes, so your take- home pay is a little lower. For your third chunk of money, the tax is a little higher, and so on. This means that the first $1000 that you make is actually $1,000, so you work for exactly the amount of money that you make. If you make $10,000, you pay some taxes, but not too much, so your take-home pay is almost the same as the amount of money that you earn. If you make $1,000,000, however, you pay a high marginal tax rate so that you might pay $0.40 in taxes on the last dollar you earn, meaning for that final dollar you put in $1 of work and got $0.60 in take-home pay. The effect of this is that as workers earn more and more money, they have less and less incentive to work: partly because they may feel that they have enough money, and partly because they have to work just as hard to get less money.

Minimum Wage

To parallel the price ceilings and floors that are sometimes set in the goods and services market, the government regulates the labor market by setting a minimum wage that firms must pay their workers. This has the same effect as a price floor. If the equilibrium wage is higher than the minimum wage (price floor), then the minimum wage has no discernable effect on the market, since the equilibrium point will be above the minimum wage. If the equilibrium wage is below the minimum wage, however, then there will be a surplus of labor: at the artificially high minimum wage, aggregate demand for labor is lower than aggregate supply, meaning that there will be unemployment (surpluses of labor). In this situation, not every worker who is willing to work for the minimum wage will be able to find a firm who wants to hire them.

Figure %: Labor Market with a Minimum Wage
So is a minimum wage worth it? There are strong arguments for either side. On one hand, if the minimum wage were removed, there might be lower unemployment, but workers might not make enough money to support themselves and their families. On the other hand, with the minimum wage in place, the employed are able to make more money, but many more workers are forced into unemployment and forced to take welfare, while making no contribution towards national productivity.

Whom does the minimum wage hurt the most? Firms will always want skilled workers who can make large contributions to productivity. When the minimum wage is installed, however, it is the least productive workers who are cut from payrolls first. The skilled workers will keep their jobs, perhaps even with higher pay; but the unskilled workers, because their MRP is lower than the new minimum wage, will be unemployed. The irony of the situation is that most people who advocate a higher minimum wage are hoping to help out the workers at the bottom of the ladder, when in reality, a higher minimum wage could very well put those workers out of a job.

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