# If Inverse Demand is P=10.5−4.99Q, what is the equation for the price-elasticity of demand? (Round to two decimals if necessary.) ϵ(P)=?

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- Anonymous8 months ago
ϵ = -(P/Q)(dQ/dP) (e.g. see link)

To get ϵ as a function of P only, i.e. ϵ(P), we need P/Q iand dQ/dP in terms of P and constants.

P=10.5−4.99Q

4.99Q = 10.5 - P

Q = 10.5/4.99 – P/4.99

. . = 2.104 – 0.2004P (equation 1)

Q/P = 2.104/P – 0.2004

. . . .= (2.104 – 0.2004P)/P

P/Q = P/(2.104 – 0.2004P)

From equation 1, dQ/dP = -0.2004

ϵ(P) = -(P/Q)(dQ/dP)

. . . .= -(P/(2.104 – 0.2004P))(-0.2004)

. . . .= 0.2004P/(2.104 – 0.2004P)

Rounded to 2d.p. this is: ϵ(P) = 0.20P/(2.10 – 0.20P)

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