Answer:
a) 20
b) elastic
c) 8
d) elastic
Explanation:
Given that q = f ( p ) = [tex]200e^{-0.4p}[/tex]
[tex]\frac{dq}{dp} = -80e^{-0.4p}[/tex]
a) The elasticity of demand is given as:
Elasticity of demand = [tex]\frac{dq}{dp}*\frac{p}{q}[/tex]
At p =$50, [tex]\frac{dq}{dp} = -80e^{-0.4p}=-80e^{-0.4*50}=-1.65*10^{-7}[/tex]
q = f ( p ) = [tex]200e^{-0.4p}[/tex] = [tex]200e^{-0.4*50}=-4.12*10^{-7}[/tex]
Elasticity of demand = [tex]\frac{dq}{dp}*\frac{p}{q}[/tex] = [tex]-1.65*10^{-7}*\frac{50}{-4.12*10^{-7}}=20[/tex]
b) At p = $50, it is elastic Since Elasticity of demand is greater than 1 it is elastic. That is the price have a big effect on the quantity
c) The elasticity of demand is given as:
Elasticity of demand = [tex]\frac{dq}{dp}*\frac{p}{q}[/tex]
At p =$20, [tex]\frac{dq}{dp} = -80e^{-0.4p}=-80e^{-0.4*20}=-0.027}[/tex]
q = f ( p ) = [tex]200e^{-0.4p}[/tex] = [tex]200e^{-0.4*20}=-0.067[/tex]
Elasticity of demand = [tex]\frac{dq}{dp}*\frac{p}{q}[/tex] = [tex]-0.027*\frac{20}{-0.067}=8.0[/tex]
d) At p = $20, it is elastic Since Elasticity of demand is greater than 1 it is elastic
