Towards a Symmetric Treatment of the Marshallian Demand Curve in the Product and Factor Market Analyses

By Awh, Robert Y. | American Economist, Spring 1994 | Go to article overview
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Towards a Symmetric Treatment of the Marshallian Demand Curve in the Product and Factor Market Analyses


Awh, Robert Y., American Economist


There will be no economist who will feel uncomfortable in giving a precise definition of a demand curve. However, the seemingly well agreed upon notion of the conventional "demand curve" becomes rather muddy when it comes to the discussion of the factor market. The purpose of this paper is to bring this puzzling phenomenon to the attention of the economics profession and suggest a remedy.

I. The Conventional Demand Curve

The notion of a Marshallian demand curve is one of the most basic and well understood concepts in economics. The demand curve shows the functional relationship between the quantity of a good demanded and its own price, ceteris paribus. In a functional form, the demand curve is shown by

[Mathematical Expression Omitted]

where [q.sub.d] is the quantity demanded, [x.sub.1] is the own price of a good and the bars above the other included variables (such as prices of related goods, income, and taste) show that they are being held constant. The well established distinction between a change in quantity demanded and a change in demand is based on the above ceteris paribus assumption included in the definition of a demand curve: If a change in [q.sub.d] is due to a change in its own price, it is a change in quantity demanded; if it is due to a change in some other variables that were held constant, it is a change in demand. Also, the celebrated law of demand, needless to say, holds under the ceteris paribus assumption inherent in the concept of a demand curve.

There is little disagreement among economists that the concept of a demand curve shows a two-variable relationship between the quantity demanded and the own price of a good while holding everything else constant. [See, for instance, Baumo] (1972), Friedman (1976), Mansfield (1988), Marshall (1890), Samuelson (1947), Schumpeter (1954), Stigler (1987).](1)

The seemingly well agreed on concept of a demand curve, however, appears to change when the discussion moves over to the factor market. In the following pages, we shall examine this asymmetry in the use of the concept of a demand curve in the product market and the factor market analyses, and suggest a remedy.

II. The Factor Demand Curve: The Conventional Treatment

One of the core topics in microeconomics at various levels of undergraduate and graduate economic education is the employment of productive factors. The conventional treatment of this subject shows that the demand curve for a factor in a competitive input market is given by the portion of its marginal revenue product MRP curve on or below its average revenue product curve.(2) Having established this, most textbooks introduce the discussion of the factor demand curve when there is a cooperating factor. The universal conclusion reached by all authors who treat this subject is that the factor demand curve in this case is given by a curve flatter than the MRP curve because the MRP curve of, say, labor following a wage reduction shifts to the right due to the increased usage of the cooperating factor, such as capital. Note that the prevalent treatment says that neither the original MRP curve nor the newly shifted MRP curve shows the factor demand curve. The factor demand curve when there is a cooperating input is given by a very different flatter curve connecting the initial equilibrium point on the original MRP curve and the equilibrium point on the new MRP curve with a larger amount of the cooperating factor. For a small sample of such a statement, see Browning and Browning (1989), Carrol (1983), Gould and Ferguson (1980), Mansfield (1991), Pindyck and Rubinfeld (1989), and Stigler (1987).

III. Does the Meaning of a Demand Curve Change in the Factor Market Analysis?

Does the flatter curve described in the preceding section--which traces the equilibrium positions on the two MRP curves before and after the factor price change--fit the definition of the generally accepted notion of a demand curve, a ceteris paribus two-variable relationship?

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