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Question
Solve the following example: If for a commodity; the demand function is given by, D = `sqrt(75 − 3"P")`. Find the marginal demand function when P = 5.
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Solution
Demand function, D =`sqrt(75 − 3"P")`
Now, Marginal demand = `("dD")/("dP")`
= `"d"/("dP")(sqrt(75 − 3"P"))`
=`1/(2 sqrt(75- 3"P")) *"d"/("dP") (75 - 3"P")`
=`1/(2 sqrt(75- 3"P"))*(0 - 3 xx1)`
=`(-3)/(2 sqrt(75 - 3"P"))`
When P = 5,
Marginal demand = `(("dD")/("dP")) _("P" = 5)`
=`(-3)/(2 sqrt(75 - 3(5)))`
= `(-3)/(2sqrt60)`
= `(-3)/(4sqrt15)`
∴ Marginal demand =`(-3)/(4sqrt15)` at P = 5.
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