i. There are K consumers enumerated as k = 1,…, K. The variable represents the quantities of factor j consumed by consumer k. This person can have endowments of good j from to . If < 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 where is the price of the good and 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 Here is the repository of all non-specified factors that affect supply for the product. The coefficient of is positive following the general rule that price and quantity supplied are directly related. is the price of a related good. Typically, its coefficient is negative because the related good is an input or a source of inputs. Movements versus shifts Movements along the curve occur only if there is a change in quantity supplied caused by a change in the good's own price. A shift in the supply curve, referred to as a change in supply, occurs only if a non-price determinant of supply changes. For example, if the price of an ingredient used to produce the good, a related good, were to increase, the supply curve would shift left. Inverse supply equation By convention in the context of supply and demand graphs, economists graph the dependent variable (quantity) on the horizontal axis and the independent variable (price) on the vertical axis. The inverse supply equation is the equation written with the vertical-axis variable isolated on the left side: . As an example, if the supply equation is then the inverse supply equation would be . Marginal costs and short-run supply curve A firm's short-run supply curve is the marginal cost curve above the shutdown point—the short-run marginal cost curve (SRMC) above the minimum average variable cost. The portion of the SRMC below the shutdown point is not part of the supply curve because the firm is not producing any output. The firm's long-run supply curve is