Supply in economics

Supply function and equation

Supply functions, then, may be classified according to the source from which they come: consumers or firms. Each type of supply function is now considered in turn. In so doing, the following notational conventions are employed: There are I produced goods, each defining a single industry, and J factors. The indices i = 1,…, I and J = 1,…, J run, respectively, over produced goods (industries) and factors. Let n index all goods by first listing produced goods and then factors so that n = 1,…, I, I + 1,…, I + J. The number of firms in industry i is written L i, and these firms are indexed by l = 1,…, L i. There are K consumers enumerated as k = 1,…, K. The variable y I + j k {\displaystyle y_{I+jk}} represents the quantities of factor j consumed by consumer k. This person can have endowments of good j from y ¯ I + 1 k {\displaystyle {\bar {y}}_{I+1k}} to y ¯ I + j k {\displaystyle {\bar {y}}_{I+jk}} . If y I + j k {\displaystyle y_{I+jk}} < y ¯ I + j k {\displaystyle {\bar {y}}_{I+jk}} then person k is a supplier of j. If the opposite is true, they are a consumer of j.
The supply function is the mathematical expression of the relationship between supply and those factors that affect the willingness and ability of a supplier to offer goods for sale. An example would be the curve implied by Q s = f ( P ; P rg ) {\displaystyle Q_{\text{s}}=f(P;P_{\text{rg}})} where P {\displaystyle P} is the price of the good and P rg {\displaystyle P_{\text{rg}}} is the price of a related good. The semicolon means that the variables to the right are held constant when quantity supplied is plotted against the good's own price. The supply equation is the explicit mathematical expression of the functional relationship. A linear example is Q s = 325 + P − 30 P rg {\displaystyle Q_{\text{s}}=325+P-30P_{\text{rg}}} Here 325 {\displaystyle 325} is the repository of all non-specified factors that affect supply for the product. The coefficient of P {\displaystyle P} is positive following the general rule that price and quantity supplied are directly related. P rg {\displaystyle P_{\text{rg}}} is the price of a related good. Typically, its coefficient is negative because the related good is an input or a source of inputs.