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Question
Find the price elasticity of demand for the demand function x = 10 – p where x is the demand p is the price. Examine whether the demand is elastic, inelastic, or unit elastic at p = 6.
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Solution
The demand function is x = 10 – p
Price elasticity of demand,
`eta_"d" = - "p"/x * "dx"/"dp"`
x = 10 - p
`"dx"/"dp"` = 0 - 1 = - 1
`eta_"d" = - "p"/x * "dx"/"dp"`
`= - "p"/(10 - "p") xx (- 1)`
`= "p"/(10 - "p")`
Price elasticity of demand when p – 6 is ηd = `6/(10 - 6) = 6/4 = 1.5`
∴ |ηd| = 1.5 > 1, the demand is elastic.
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