The price elasticity of demand for a linear demand function, D(p)=b−ap is given by Q=E(p)=(ap)/(b-ap)?

Question

Rewrite the formula to express price as a function of elasticity

p=g(Q)=?

Update:

b)  What is the long-term behavior of g?

As elasticity increases without bound, the price at which this elasticity occurs approaches

Answer 1

E= ap/(b - ap)

Eb - Eap= ap

Eap + ap= Eb

p(Ea + a)= Eb

p= g(Q)= Eb/(Ea + a)= Eb/[a(E + 1)]

As E→∞, p→b/a

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