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Marginal Productivity and Income

The basic theory for resource markets is part of the theory of the firm. Key concepts are those of marginal resource cost (MRC) and marginal revenue product (MRP). A firm maximizes profit when it sets MRC equal to MRP. Let us briefly review this result.

Firms buy resources or inputs when it is profitable to do so. A resource is valuable not because it directly satisfies some goal, but because it can indirectly satisfy a goal. Economists say that the demand for a resource is a derived demand. The demand for the resource is derived, or comes from, the demand for the goods and services that the resource produces. The benefit that a firm receives from an added input is the extra revenue it earns from selling production that the input adds. (Economists call this benefit the marginal revenue product, or MRP.)

Most inputs must be bought, hired, or rented. (Economists call the cost of an additional input the marginal resource cost, or MRC.) For a firm to make a profit from an added input, the additional revenue must exceed the additional cost. Economists take this commonsense idea and put it into economic jargon, saying that a firm should increase the use of an input if MRP exceeds MRC and reduce the use of an input when the MRC exceeds MRP. Therefore, when MRC equals MRC the firm should neither increase or decrease the input--it has found the profit-maximizing level.

To push the analysis further, assume that many firms buy the resource and that none of these firms can noticeably influence price in any market. This assumption that firms are price takers means that marginal revenue equals price of output, and that the marginal resource cost equals the price of the resource. To make the following discussion less abstract, suppose that the resource in question is hours of labor, which means that the price in this market will be wages.

With these assumptions, we get a diagram similar to that can be used to explain the technicalities of economic efficiency. On the left is Peter Milloy, a representative worker who sells hours of unskilled labor. His supply curve is drawn so that it slopes upward. But he is only one of a great many workers selling in this market. To find the market supply curve, one must add up all the hours of work that will be offered at each wage.

The labor market

On the right is Dynamic Enterprises, one of a great many buyers of unskilled labor. Its demand curve will be the downward-sloping part of its MRP curve. The MRP curve is the demand curve for labor because this curve tells how valuable another unit of the resource is to the firm. Hence, given a wage, one can tell how much labor a firm demands by looking at the MRP curve.

Dynamic Enterprises is only one of a great many buyers of labor. To find the market demand, one must add up at each wage the number of labor hours demanded by each firm. The intersection of the market demand and market supply curve gives the equilibrium wage--it will hire all workers who contribute more to the firm than they cost.

This simple analysis develops what economists call the marginal productivity theory of wages: in a competitive market owners of resources tend to be paid their marginal contribution to output. An owner of a resource that adds a more valuable contribution to output is paid more than an owner of resource that adds a less valuable contribution. The key words here are "marginal" and "adds." For example, garbage collectors perform a vital service in large cities, and when they go on strike, people are not only tremendously inconvenienced, but their health may be threatened. The total value of the services of garbage collectors is very high. But this high total value does not mean that the value of another garbage collector is high. If adding or removing one garbage collector changes the value of garbage collection services little, his marginal contribution will give a low wage in this market. This analysis exactly parallels the diamond-water paradox.

The graphs above help illustrate changes that will raise or lower wages or other payments to inputs. The demand curve could shift because people value the output more. For example, the high salaries of professional basketball players are due to the popularity of basketball as a spectator sport. A century ago, a man with the same abilities of a Larry Bird or a Michael Jordan would have earned a normal income because there was no demand for his special talents.

Increased productivity can also shift the demand curve. Industrialized societies has created a vast number of complex machines. Much of this capital is a substiture for unskilled physical labor but complements skilled intellectual labor. As a result, the rewards going to muscle power have fallen compared to the rewards going to brain power. Two hundred years, ago a strong but stupid man would probably have earned more than his smart but lame brother. Today, the results would probably be reversed.

The supply curve can also change, and as it does, so will the income that the resource earns. A new discovery of metal ore will reduce the value of known deposits. Increased availability of education increases the numbers of doctors, lawyers, teachers, and accountants. If demand for their services does not change, their increased numbers will cause their incomes to drop. People who want to control the wages they earn have usually tried to control the supply curve by limiting competition.

Real-world economies are not the same as abstract, theoretical economies. Real-world economies have factors other than productivity that determine income. For example, when people are engaged in what economists call rent seeking (something that does not exist in an ideal competitive economy), there may be a negative correlation between how much people earn and their socially useful productivity. However, even in theoretical market economies there are reasons, which will be discussed shortly, why income may not reflect marginal productivity.

But first we see how the marginal productivity argument that we have developed is key to explaining real wages.

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Copyright Robert Schenk