, an excess demand function
is a function expressing excess demand
for a product—the excess of quantity demanded over quantity supplied—in terms of the product's price
and possibly other determinants.
It is the product's demand function
minus its supply function
. In a pure exchange economy
, the excess demand is the sum of all agents' demands minus the sum of all agents' initial endowments.
A product's excess supply function
is the negative of the excess demand function—it is the product's supply function minus its demand function. In most cases the first 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 the equilibrium price
if it is such that the value of the excess demand function is zero: that is, when the market is in equilibrium
, meaning that the quantity supplied equals the quantity demanded. In this situation it is said that the market clears
. If the price is higher than the equilibrium price, excess demand will normally be negative, meaning that there is a surplus
(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 a shortage
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.
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.
If continuous time
is assumed, the adjustment process is expressed as a differential equation
is the price, f
is the excess demand function, and 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 is stable
provided the derivative of f
with respect to P
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.
is the discrete-time analog of the continuous time expression
, and where 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
Last edited on 12 April 2021, at 04:45
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