In
microeconomics
Microeconomics is a branch of mainstream economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms. Microeconomics fo ...
, excess demand is a phenomenon where the demand for goods and services exceeds that which the firms can produce.
In
microeconomics
Microeconomics is a branch of mainstream economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms. Microeconomics fo ...
, an excess demand function is a function expressing
excess demand
In economics, a shortage or excess demand is a situation in which the demand for a product or service exceeds its supply in a market. It is the opposite of an excess supply (surplus).
Definitions
In a perfect market (one that matches a sim ...
for a product—the excess of quantity demanded over quantity supplied—in terms of the product's
price
A price is the (usually not negative) quantity of payment or compensation given by one party to another in return for goods or services. In some situations, the price of production has a different name. If the product is a "good" in the c ...
and possibly other determinants. It is the product's
demand function
In economics, a demand curve is a graph depicting the relationship between the price of a certain commodity (the ''y''-axis) and the quantity of that commodity that is demanded at that price (the ''x''-axis). Demand curves can be used either for ...
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
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
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
In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the ( equilibrium) values of economic variables will not change. For example, in the st ...
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
In economics, a shortage or excess demand is a situation in which the demand for a product or service exceeds its supply in a market. It is the opposite of an excess supply ( surplus).
Definitions
In a perfect market (one that matches a si ...
.
Walras' law
Walras's law is a principle in general equilibrium theory asserting that budget constraints imply that the ''values'' of excess demand (or, conversely, excess market supplies) must sum to zero regardless of whether the prices are general equilib ...
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.
Market dynamics
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
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled.
Discrete time
Discrete time views values of variables as occurring at distinct, separate "po ...
is assumed, the adjustment process is expressed as a
differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
such as
:
where ''P'' 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.
If the market is analyzed in
discrete time
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled.
Discrete time
Discrete time views values of variables as occurring at distinct, separate "po ...
, then the dynamics are described by a
difference equation such as
:
where
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
.
Sonnenschein–Mantel–Debreu theorem
The Sonnenschein–Mantel–Debreu theorem is an important result concerning excess demand functions, proved by
Gérard Debreu, , and
Hugo F. Sonnenschein in the 1970s. It states that the excess demand curve for a market populated with
utility-maximizing rational agents
A rational agent or rational being is a person or entity that always aims to perform optimal actions based on given premises and information. A rational agent can be anything that makes decisions, typically a person, firm, machine, or software. ...
can take the shape of any
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
that is
continuous
Continuity or continuous may refer to:
Mathematics
* Continuity (mathematics), the opposing concept to discreteness; common examples include
** Continuous probability distribution or random variable in probability and statistics
** Continuous ...
,
homogeneous of degree zero, and in accord with
Walras's law
Walras's law is a principle in general equilibrium theory asserting that budget constraints imply that the ''values'' of excess demand (or, conversely, excess market supplies) must sum to zero regardless of whether the prices are general equilib ...
. This implies that market processes will not necessarily reach a unique and stable
equilibrium point, because the excess demand curve need not be downward-sloping.
References
Bibliography
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Demand