Question

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.

Answer 1

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