Advertisement Remove all ads

# If the demand function is D = (p+6p-3), find the elasticity of demand at p = 4. - Mathematics and Statistics

Sum

If the demand function is D = (("p" + 6)/("p" - 3)), find the elasticity of demand at p = 4.

Advertisement Remove all ads

#### Solution

Given, demand function is

D = (("p" + 6)/("p" - 3))

∴ "dD"/"dp" = (("p" - 3) "d"/"dp" ("p" + 6) - ("p" + 6) "d"/"dp" ("p" - 3))/("p" - 3)^2

= (("p" - 3)(1 + 0) - ("p" + 6)(1 - 0))/("p" - 3)^2

∴ "dD"/"dp" = ("p" - 3 - "p" - 6)/("p" - 3)^2

= (-9)/("p" - 3)^2

eta = (-"p")/"D" * "dD"/"dp"

∴ eta = (- "p")/((("p" + 6)/("p" - 3))) * (-9)/("p" - 3)^2

∴ eta = (9"p")/(("p" + 4)("p" - 3))

Substituting p = 4, we get

eta = (9 xx 4)/((4 + 6)(4 - 3)) = 36/(10(1))

∴ η = 3.6

∴ elasticity of demand at p = 4 is 3.6

Concept: Application of Derivatives to Economics
Is there an error in this question or solution?
Advertisement Remove all ads

#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 4 Applications of Derivatives
Exercise 4.4 | Q 8 | Page 112
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?