Suppose we have the following hypothetical demand function:
Qx = 600 - 3px + 0.04I - 2pz
Where Px = $ 70, Pz = 68, I = $ 24,000 (disposable income per capita).
What is the demand equation? The price of product X, Px = 70. Calculate the price point elasticity of demand.
The demand equation is a linear equation and it defines the algebraic representation of quantity and price of product. The form of equation of linear function is the following, such that:
`P(x) = a*x + b`
The price point elasticity of demand can be evaluated using derivative of demand function Q, with respect to price P, such that:
Point Price Elasticity of Demand = `(Delta Q)/(Delta P)`
Given `Q(x) = 600 - 3P(x) + 0.04I - 2P(z)` and differentiating Q with respect to x, yields:
`(Delta Q)/(Delta P) = -3`
Hence, the quantity goes down by 3, each time the price goes up by 1.
Evaluating the point price elasticity of demand at P =70, yields:
`e = -3*70/(600 - 3*70 + 0.04*24000 - 2*68)`
`e = -210/(600 - 210 + 960 - 136)`
`e = -210/1214 => e = -0.172`
Hence, evaluating the point price elasticity of demand at P =70, yields ` e = -0.172.`