Inmicroeconomics, excess demand, also known asshortage, is a phenomenon where the demand for goods and services exceeds that which the firms can produce.

Inmicroeconomics, anexcess demand function is a function expressing excess demand for a product—the excess of quantity demanded over quantity supplied—in terms of the product'sprice and possibly other determinants.^[1] It is the product'sdemand function minus itssupply function. In a pureexchange economy, the excess demand is the sum of all agents' demands minus the sum of all agents' initial endowments.

A product'sexcess supply function is the negative of the excess demand function—it is the product's supply function minus its demand function. In most cases thefirst derivative of excess demand with respect to price is negative, meaning that a higher price leads to lower excess demand.

The price of the product is said to be theequilibrium price if it is such that the value of the excess demand function is zero: that is, when the market is inequilibrium, meaning that the quantity supplied equals the quantity demanded. In this situation it is said that themarketclears. If the price is higher than the equilibrium price, excess demand will normally be negative, meaning that there is asurplus (positive excess supply) of the product, and not all of it being offered to the marketplace is being sold. If the price is lower than the equilibrium price, excess demand will normally be positive, meaning that there is ashortage.

Walras' law implies that, for every price vector, the price–weighted total excess demand is 0, whether or not the economy is in general equilibrium. This implies that if there is excess demand for one commodity, there must be excess supply for another commodity.

The concept of an excess demand function is important in general equilibrium theories, because it acts as a signal for the market to adjust prices.^[2] The assumption is that the rate of change of the price of a commodity will be proportional to the value of the excess demand function for that commodity, eventually leading to an equilibrium state in which excess demand for all commodities is zero.^[3] Ifcontinuous time is assumed, the adjustment process is expressed as adifferential equation such as

${\displaystyle \frac{dP}{dt}=\lambda \cdot f(P,...)}$

whereP is the price,f is the excess demand function, and${\displaystyle \lambda }$ is the speed-of-adjustment parameter that can take on any positive finite value (as it goes to infinity we approach the instantaneous-adjustment case). This dynamic equation isstable provided the derivative off with respect toP is negative—that is, if a rise (or, fall) in the price decreases (or, increases) the extent of excess demand, as would normally be the case.

If the market is analyzed indiscrete time, then the dynamics are described by adifference equation such as

${\displaystyle P_{t+1}=P_t+\delta \cdot f(P_t,...)}$

where${\displaystyle P_{t+1}-P_t}$ is the discrete-time analog of the continuous time expression${\displaystyle \frac{dP}{dt}}$, and where${\displaystyle \delta }$ is the positive speed-of-adjustment parameter which is strictly less than 1 unless adjustment is assumed to take place fully in a single time period, in which case${\displaystyle \delta =1}$.

The Sonnenschein–Mantel–Debreu theorem is an important result concerning excess demand functions, proved byGérard Debreu,Rolf Mantel [es], andHugo F. Sonnenschein in the 1970s.^[4][5][6][1] It states that the excess demand curve for a market populated withutility-maximizingrational agents can take the shape of anyfunction that iscontinuous,homogeneous of degree zero, and in accord withWalras's law.^[7] This implies that market processes will not necessarily reach a unique and stableequilibrium point,^[8] because the excess demand curve need not be downward-sloping.

• Demand