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Question
If the demand law is given by p = `10e^(- x/2)` then find the elasticity of demand.
Solution
p = `10e^(- x/2)`
Elasticity of demand: ηd = `- p/x * "dx"/"dp"`
p = `10e^(- x/2)`
`"dp"/"dx" = 10(e^(-x/2))(- 1/2)`
`= - 10/2 e^(-x/2)`
`= - 5e^(-x/2)`
Elasticity of demand: ηd = `- p/x * 1/("dp"/"dx")`
`= ((- 10e^(-x/2))/x)(1/(- 5e^(-x/2)))`
`= (-10)/(-5x) xx e^(-x/2)/e^(-x/2)`
ηd = `2/x`
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