Supply (economics)

A supply schedule is a table which shows how much one or more firms will be willing to supply at particular prices under the existing circumstances.[1] Some of the more important factors affecting supply are the good's own price, the prices of related goods, production costs, technology, the production function, and expectations of sellers.

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 ${\displaystyle y_{I+jk}}$represents the quantities of factor j consumed by consumer k. This person can have endowments of good j from ${\displaystyle {\bar {y}}_{I+1k}}$to ${\displaystyle {\bar {y}}_{I+jk}}$. If ${\displaystyle y_{I+jk}}$ < ${\displaystyle {\bar {y}}_{I+jk}}$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 ${\displaystyle Q_{\text{s}}=f(P;P_{\text{rg}})}$ where ${\displaystyle P}$ is the price of the good and ${\displaystyle P_{\text{rg}}}$ 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 ${\displaystyle Q_{\text{s}}=325+P-30P_{\text{rg}}}$ Here ${\displaystyle 325}$ is the repository of all non-specified factors that affect supply for the product. The coefficient of ${\displaystyle P}$ is positive following the general rule that price and quantity supplied are directly related. ${\displaystyle P_{\text{rg}}}$ is the price of a related good. Typically, its coefficient is negative because the related good is an input or a source of inputs.

Movements along the curve occur only if there is a change in quantity supplied caused by a change in the good's own price.[10] A shift in the supply curve, referred to as a change in supply, occurs only if a non-price determinant of supply changes.[10] 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.[11]

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: ${\displaystyle P=f(Q)}$. As an example, if the supply equation is ${\displaystyle Q=40P-2P_{rg}}$ then the inverse supply equation would be ${\displaystyle P={\tfrac {Q}{40}}+{\tfrac {P_{rg}}{20}}}$.[12]

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.[13] The firm's long-run supply curve is that portion of the long-run marginal cost curve above the minimum of the long run average cost curve.

The Law of Diminishing Marginal Returns (LDMR) shapes the SRMC curve. The LDMR states that as production increases eventually a point (the point of diminishing marginal returns) will be reached after which additional units of output resulting from fixed increments of the labor input will be successively smaller. That is, beyond the point of diminishing marginal returns the marginal product of labor will continually decrease and hence a continually higher selling price would be necessary to induce the firm to produce more and more output.

The market supply curve is the horizontal summation of firm supply curves.[14]

The market supply curve can be translated into an equation. For a factor j for example the market supply function is

${\displaystyle S_{j}=S^{j}(p,r)}$

where

${\displaystyle S_{j}=\sum _{k=1}^{j}S_{jk}}$ and ${\displaystyle S^{j}(p,r)=\sum _{k=1}^{j}S^{jk}(p,r)}$ for all p > 0 and r > 0.

Note: not all assumptions that can be made for individual supply functions translate over to market supply functions directly.

The law of supply dictates that all other things remaining equal, an increase in the price of the good in question results in an increase in quantity supplied. In other words, the supply curve slopes upwards.[15] However, there are exceptions to the law of supply. Not all supply curves slope upwards.[16]

Some heterodox economists, such as Steve Keen and Dirk Ehnts, dispute this theory of the supply curve, arguing that the supply curve for mass produced goods is often downward-sloping: as production increases, unit prices go down, and conversely, if demand is very low, unit prices go up.[17][18] This corresponds to economies of scale.

The price elasticity of supply (PES) measures the responsiveness of quantity supplied to changes in price, as the percentage change in quantity supplied induced by a one percent change in price. It is calculated for discrete changes as ${\displaystyle \left({\tfrac {\Delta Q}{\Delta P}}\right)\times {\tfrac {P}{Q}}}$ and for smooth changes of differentiable supply functions as ${\displaystyle \left({\tfrac {\partial Q}{\partial P}}\right)\times {\tfrac {P}{Q}}}$. Since supply is usually increasing in price, the price elasticity of supply is usually positive. For example, if the PES for a good is 0.67 a 1% rise in price will induce a two-thirds increase in quantity supplied.

Significant determinants include:

Complexity of production: Much depends on the complexity of the production process. Textile production is relatively simple. The labor is largely unskilled and production facilities are little more than buildings—no special structures are needed. Thus, the PES for textiles is elastic. On the other hand, the PES for specific types of motor vehicles is relatively inelastic. Auto manufacture is a multi-stage process that requires specialized equipment, skilled labor, a large suppliers network and large R&D costs.

Time to respond: The more time a producer has to respond to price changes the more elastic the supply. For example, a cotton farmer cannot immediately respond to an increase in the price of soybeans.

Excess capacity: A producer who has unused capacity can quickly respond to price changes in his market assuming that variable factors are readily available.

Inventories: A producer who has a supply of goods or available storage capacity can quickly respond to price changes.

Other elasticities can be calculated for non-price determinants of supply. For example, the percentage change the amount of the good supplied caused by a one percent increase in the price of a related good is an input elasticity of supply if the related good is an input in the production process. An example would be the change in the supply of cookies caused by a one percent increase in the price of sugar.

There is no such thing as a monopoly supply curve.[21] Perfect competition is the only market structure for which a supply function can be derived. In a perfectly competitive market the price is given by the marketplace from the point of view of the supplier; a manager of a competitive firm can state what quantity of goods will be supplied for any price by simply referring to the firm's marginal cost curve. To generate his supply function the seller could simply initially hypothetically set the price equal to zero and then incrementally increase the price; at each price he could calculate the hypothetical quantity supplied using the marginal cost curve. Following this process the manager could trace out the complete supply function. A monopolist cannot replicate this process because price is not imposed by the marketplace and hence is not an independent variable from the point of view of the firm; instead, the firm simultaneously chooses both the price and the quantity subject to the stipulation that together they form a point on the customers' demand curve. A change in demand can result in "changes in price with no changes in output, changes in output with no changes in price or both".[21] There is simply not a one-to-one relationship between price and quantity supplied.[22] There is no single function that relates price to quantity supplied.

Supply curve

• Demand curve
• Law of supply
• Profit maximization