Supply in economics

From firm to market supply curve

The market supply curve is the horizontal summation of firm supply curves.^[15]
The market supply curve can be translated into an equation. For a factor j for example the market supply function is
S j = S j ( p , r ) {\displaystyle S_{j}=S^{j}(p,r)}
where
S j = ∑ k = 1 k S j k {\displaystyle S_{j}=\sum _{k=1}^{k}S_{jk}} and S j ( p , r ) = ∑ k = 1 k S j k ( p , r ) {\displaystyle S^{j}(p,r)=\sum _{k=1}^{k}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 shape of the market supply curve

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.^[16] However, there are exceptions to the law of supply. Not all supply curves slope upwards.^[17]
Empirical data, however, shows that the supply curve for mass produced goods is often downwardsloping. As production increases, unit prices go down. And, conversely, if demand is very low, unit prices go up. This corresponds to economies of scale.^[18]

Elasticity

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 ( Δ Q Δ P ) × P Q {\displaystyle \left({\tfrac {\Delta Q}{\Delta P}}\right)\times {\tfrac {P}{Q}}} and for smooth changes of differentiable supply functions as ( ∂ Q ∂ P ) × P Q {\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: