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.
Thanks SO much :))
BTW, E(p)=-(pf'(p))/(f(p) Thanks!
- Snrpatel10Lv 66 years agoFavorite Answer
Equation for Elasticity of Demand:
E(P) = (dQ/dP)*(P/Q)
(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
Demand is Price Inelastic when P = 13
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