Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 years ago

# Elasticity of demand problem (calculus)?

Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p.

x=f(p)=2005-p^2; p=13

Thanks SO much :))

Update:

BTW, E(p)=-(pf'(p))/(f(p) Thanks!

Relevance
• 6 years ago

Equation for Elasticity of Demand:

E(P) = (dQ/dP)*(P/Q)

Where:

(dQ/dP) = derivative of the demand function

P = Price

Q = Quantity

The demand function we're given is:

x = 2005 - P²

And the question is asking us to determine whether demand is elastic, inelastic, or is unit elastic when the price is \$13.

We first start by taking the derivative of the demand function, which we can easily do by applying the power rule. Taking the derivative of the demand function will give us:

x = 2005 - P²

dx/dP = -2P

Plugging in what we know into the Elasticity of Demand equation will give us:

E(P) = (dx/dP)*(P/x)

E(P) = (-2P)*(P/x)

Since we're told that x = 2005 - P², we can substitute 2005 - P², for x, in the Elasticity of Demand equation. Doing so will give us:

E(P) = (-2P)*(P / 2005 - P²)

Multiplying through by P will give us:

E(P) = (-2P²) / (2005 - P²)

Plugging 13 in for all values of P will give us:

E(13) = (-2(13)²) / (2005 - (13)²)

E(13) = -338 / 1836

E(13) = -169 / 918 = -.184096

Because -.184096 is greater than -1 but less than 0, demand is therefore inelastic when P = 13