Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# The demand for a quantity A is q = pp80-p12+5p2. Find the partial elasticities EqEpEqEp1 and EqEpEqEp2 when p1 = 2, p2 = 1. - Business Mathematics and Statistics

Sum

The demand for a quantity A is q = 80 - "p"_1^2 + 5"p"_2 - "p"_1"p"_2. Find the partial elasticities "E"_"q"/("E"_("p"_1)) and "E"_"q"/("E"_("p"_2))  when p1 = 2, p2 = 1.

#### Solution

q = 80 - "p"_1^2 + 5"p"_2 - "p"_1"p"_2

(del"q")/(del"p"_1) = 0 - 2"p"_1 + 0 - (1)"p"_2

= - 2"p"_1 - "p"_2

(del"q")/(del"p"_2)= 0 - 0 + 5(1) - p1 (1)

= 5 - p1

therefore "E"_"q"/(del_("p"_1)) = - "p"_1/"q" (del"q")/(del"p"_1)

= (- "p"_1)/(80 - "p"_1^2 + 5"p"_2 - "p"_1"p"_2) xx (- 2"p"_1 - "p"_2)

When p1 = 2, p2 = 1,

"E"_"q"/(del_("p"_1)) = ((-2)/(80 - 2^2 + 5(1) - 2 xx 1)) (- 2 xx 2 - 1)

= (-2)/(80 - 4 + 5 - 2) xx (- 4 - 1) = 10/79

"E"_"q"/("E"_("p"_2)) = - "p"_2/"q" (del"q")/(del"p"_2)

= (- "p"_2)/(80 - "p"_1^2 + 5"p"_2 - "p"_1"p"_2) (- 5"p"_1)

When p1 = 2, p2 = 1,

"E"_"q"/("E"_("p"_2)) = (-1)/(80 - 2^2 + 5 xx 1 - 2xx1) (5 - 2)

= (-1)/79 xx (3) = (-3)/79

Concept: Applications of Partial Derivatives
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