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Question
If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.
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Solution
Given, D =` ("P"+ 5)/("P" - 1)`
Marginal demand =`("dD")/("dP")= "d"/("dP")(("P"+ 5)/("P" - 1))`
= `(("P" - 1)"d"/("dP")("P"+ 5) - ("P"+ 5)"d"/("dP")("P" - 1))/("P" - 1)^2`
= `(("P" - 1)(1 + 0) - ("P"+ 5)(1 - 0))/("P" - 1)^2`
=`("P" - 1 - "P" - 5)/(("P" - 1)^2`
=`(-6)/(("P" - 1)^2`
When P = 2,
Marginal demand,`(("dP")/("dP"))_("P" = 2) =(-6)/(2 - 1)^2 = -6`
∴ When price is 2, marginal demand is – 6.
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