Question

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.

Answer 1

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`