Consider the following demand curve Qd 240 4P What is the

Consider the following demand curve: Qd = 240 - 4P What is the price elasticity of demand at $45 What is the price elasticity of demand at $30 What is the price elasticity of demand at $15

Solution

We can calculate any elasticity by the formula:

Elasticity of Z with respect to Y = (dZ / dY) *(Y / Z).

We can use the above demand function thus: (dQ / dP) * (P / Q). In order to use the equation, we must have quantity alone on the left-hand side, and the right-hand side by some function of price.

Thus we differentiate with respect to P and get dQ / dP = -4.

Now we substitute dQ / dP = -4 and Q = 240 -4P into our price elasticity of demand equation.

# Price elasticity of demand = (dQ / dP) * (P / Q)

# Price elasticity of demand = (-4) * (P / (240 - 4P)

# Price elasticity of demand = -4P / (240 – 4P)

#1. The price elasticity of demand at $45 = -4*45 / 240 – (45 x 4)

#1. Price elasticity of demand at $45 = -180 / 60 = - 3

#2. Price elasticity of demand at $30 = -4*30 / 240 – (30 x 4)

#2. Price elasticity of demand at $30 = - 120 / 120 = - 1.

# 3. Price elasticity of demand at $15 = -4 * 15 / 240 – (15 x 4)

#3. Price elasticity of demand at $15 = - 60 / 180 = - 1 / 3.

*****