Question

The supply function of certain goods is given by x = a`sqrt("p" - "b")` where p is unit price, a and b are constants with p > b. Find elasticity of supply at p = 2b.

Answer 1

Given that x = a`sqrt("p" - "b")`

Elasticity of supply: η_s = `"p"/x * "dx"/"dp"`

x = a`sqrt("p" - "b")`

`"dx"/"dp" = "a"(1/(2sqrt "p - b"))`

η_s = `"p"/x * "dx"/"dp"`

`= "p"/("a"sqrt("p" - "b")) xx "a" xx 1/(2sqrt("p" - "b"))`

`= "p"/(2("p - b"))`

Hint for differentiation

Use y = `sqrtx`

`"dy"/"dx" = 1/(2sqrtx)`

(or) x = `"a"sqrt("p - b")`

x = `"a"("p - b")^(1/2)`

`"dx"/"dp" = "a" * 1/2 ("p - b")^(1/2 - 1)`

`= "a"/2 ("p - b")^(- 1/2)`

`= "a"/2 1/(sqrt ("p - b"))`

When p = 2b, Elasticity of supply: η_s = `"2b"/(2("2b" - "b")) = "2b"/"2b" = 1`