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Question
Find out the indicated elasticity for the following function:
p = `10 e^(- x/3)`, x > 0; ηs
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Solution
Given p = `10 e^(- x/3)`
Differentiating with respect to 'x' we get,
`"dp"/"dx" = 10 * e^(-x/3) (- 1/3) = - 10/3 e^(- x/3)`
`=> "dp"/"dx" = (-3)/(10e^(-x/3))`
`=> "dx"/"dp" = (-3)/(10e^(-x/3))`
Elasticity of demand
`eta_"d"= - "p"/x * "dx"/"dp"`
`=> eta_"d"= cancel(-10 e^(- x/3))/x ((-3)/(cancel(10e^(-x/3)))) = 3/x`
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