Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# The demand for a quantity A is q = pp13-2p1-3p22. Find the partial elasticities EqEpEqEp1 and EqEpEqEp2 when p1 = p2 = 2. - Business Mathematics and Statistics

Sum

The demand for a quantity A is q = 13 - 2"p"_1 - 3"p"_2^2. Find the partial elasticities "E"_"q"/("E"_("p"_1)) and "E"_"q"/("E"_("p"_2))  when p1 = p2 = 2.

#### Solution

q = 13 - 2"p"_1 - 3"p"_2^2

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

(del"q")/(del"p"_2)= 0 - 0 - 3(2)p2 = - 6p2

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

= (- "p"_1)/(13 - 2"p"_1 - 3"p"_2^2)(- 2)

When p1 = p2 = 2,

"E"_"q"/("E"_("p"_1)) = ((-2)/(13 - 2 xx 2 - 3 xx 2^2))(-2)

= (- 2 xx -2)/(13 - 4 - 3 xx 4)

= 4/(13 - 4 - 12)

= 4/(13 - 16)

= 4/(- 3) = (-4)/3

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

= (- "p"_2)/(13 - 2"p"_1 - 3"p"_2^2) (- 6"p"_2)

When p1 = p2 = 2,

"E"_"q"/("E"_("p"_2)) = ((-2)/(13 - 2 xx 2 - 3 xx 2^2)) (- 6 xx 2)

= (- 2 xx -12)/(13 - 4 - 12)

= 24/(-3) = -8

Concept: Applications of Partial Derivatives
Is there an error in this question or solution?