The Supply Function

As stated in the text, the basic determinants of market supply for a specific good such as Q₁ are (1) resource prices, which we can denote by P_R1, P_R2, and so on; (2) the state of technology, T; (3) the number of producers in the market, N; (4) taxes and subsidies, S₁, S₂, and so on; and (4) the prices of related goods, P₂, P₃, and so on.

Consider a typical firm, which we will denote with the subscript "i." This firm produces some amount of good Q₁ which provides it with the greatest profit. This amount will of course vary, depending on the price of good Q₁, the prices of its inputs, the available technology, taxes and subsidies, and the prices of related goods. We can write this relationship as: = g_i(P₁; P_R1, P_R2, ...; P₂, P₃, ...; S₁, S₂, ...; T_i). This individual’s supply curve for good Q₁ is found by holding constant the value of all variables other than the price of good Q₁ and graphing the resulting relationship between and P₁. This relationship is typically written = g_i(P₁|P_R1, P_R2, ...; P₂, P₃ , ...; S₁, S₂, ...; T_i).

There are N firms, each of whom have similar supplies for good Q₁. The market supply for this good is simply the sum of all of the quantities supplied by the N firms at each possible price:

Q₁ = = g_i(P₁| P_R1, P_R2, ...; P₂, P₃ , ...; S₁, S₂, ...; T_i). For simplicity, this can be written as Q₁ = G₁(P₁|P_R, P₂, S, T, N).

Written in this form, the function clearly shows that the market supply for a good is a relationship between the quantity supplied of a good and its price, holding constant the prices of its resources, the prices of all other goods, subsidies and taxes, the state of technology, and the number of suppliers. A change in any of the factors previously held constant will result in a different relationship between Q₁ and P₁. We would call this new relationship a change in supply.