# 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...

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.

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### 1 Answer

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.`