Residual demand

The residual demand (from Latin : residuum = remainder) is a term from microeconomics . The residual demand is the demand for a good in a market at a certain price, which cannot be satisfied by the supply of the competitors.

In order to grasp this verb definition mathematically, consider a function that depends on an influencing variable. In microeconomics, the notation is usually chosen for the demand function and the supply function , the influencing factors of which are the price . ${\displaystyle y=f(x)\,}$ ${\displaystyle x\,}$ ${\displaystyle D\,}$ ${\displaystyle S\,}$ ${\displaystyle p\,}$

The notation is used for the residual demand function. Under the transitivity assumption and the completeness assumption in microeconomics, the demand for a good for an individual company can be determined. ${\displaystyle D_{r}(p)\,}$

With a given (market) demand function and a given supply function of the other competitors in the market , the residual demand can be calculated for an individual company as follows. ${\displaystyle D(p)\,}$ ${\displaystyle S(p)\,}$

${\displaystyle D_{r}(p)=D(p)-S(p)\,}$

As the number of competitors increases , the demand curve in the market becomes more elastic . The elasticity of the residual demand curve gives the company information about the behavior of competitors when prices change. ${\displaystyle n\,}$

The following applies to the elasticity of the residual demand:

${\displaystyle {\frac {\partial D_{r}}{\partial p}}\cdot {\frac {q}{p}}={\frac {\partial D}{\partial p}}\cdot {\frac {q}{p}}-{\frac {\partial S_{r}}{\partial p}}\cdot {\frac {q}{p}}}$

${\displaystyle {\frac {\partial D_{r}}{\partial p}}\cdot {\frac {q}{p}}={\frac {\partial D}{\partial p}}\cdot {\frac {p}{Q}}\cdot {\frac {Q}{p}}-{\frac {\partial S_{r}}{\partial p}}\cdot {\frac {p}{Q_{0}}}\cdot {\frac {Q_{0}}{p}}}$

With

${\displaystyle Q\,}$, = Total quantity of the offered good on the market;

${\displaystyle q\,}$, = Amount of goods offered by company i;

${\displaystyle Q0\,}$, = Quantity of goods offered by all other companies (except company i)

Under the simplified assumption that all other companies produce the same amount, the elasticity of the residual demand results: ${\displaystyle q=Q/n\,}$

${\displaystyle \epsilon _{i}=\epsilon n-\eta _{0}(n-1)\,}$

With

${\displaystyle \epsilon _{i}\,}$as the elasticity of demand and as the elasticity of the residual supply curve. ${\displaystyle \eta _{0}\,}$

See also

To interpret elasticity: price elasticity

literature

• Hal R. Varian : Fundamentals of Microeconomics . Oldenbourg Verlag, ISBN 3-486-27453-8