|San José State University|
& Tornado Alley
and Consumer Income
Demand functions gives the quantities purchased as functions of prices. Let X be the column vector of consumer goods and P the column vector of prices. Consumer income will be denoted as y. The demand functions are
The choices are constrained to satisfy the condition
where PT is the transpose of P.
The inverse demand function for the j-th good or service is
Very little can be said about inverse demand functions except that they are downward sloping. However what else can be said is that if income and all other prices are increaed by a factor (1+γ) then the inverse demand curve for the j-th good or service will also be shifted upward by a factor (1+γ). This is because
Functions like F(P, y) are said to homogeneous to degree zero.
If incomes are determined by the supply of labor services and R is the vector of labor wage rates then
If L is the vector of labor services supplied and incomes are given by
then all wage rates and all prices for all goods and services except the j-th one are increased by a factor of (1+γ) then the inverse demand for the j-th good or services also increases by a factor of (1+γ).
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