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Question
If the demand function is D = 50 - 3p - p2, find the elasticity of demand at (a) p = 5 (b) p = 2 , Interpret your result.
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Solution
D = 50 - 3p - p2
`therefore "dD"/"dp" = - 3 - 2p`
Elasticity of demand η
`= -"P"/"D" . "dD"/"dp"`
`= -"p"/(50 - 3"p" - "p"^2) xx (- 3 - 2"p")`
`= ((3 + 2"p")"p")/(50 - 3"p" - "p"^2)`
(a) When p = 5 , η = `65/10` = 6.5 > 1
∴ η is elastic.
(b) When p = 2 , η = `14/40 = 7/20 < 1`
∴ η is inelastic .
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