Question

Can someone help me please
A general exponential demand function has the form q = Ae^−bp (A and b nonzero constants).

(a) Obtain a formula for the price elasticity E of demand at a unit price of p.
(b) Obtain a formula for the price p that maximizes revenue.

Answer 1

elasticity=%(change in quantity)/%(change in quantity)

Answer 2

when you start to calculate
change in quantity=dq
change in price =dp

Answer 3

so %change in quantity=100*(dq/q)
%change in price=100*(dp/p)

Answer 4

therefore =>e=(100*dq/q)/100*(dp/p)
e=(dq/q)*(p/dp)
e=(dq/dp)*(p/q)

Answer 5

now q=Ae^(-bp)
dq/dp=A*-b*e^(-bp)
e=p/q*A*-b*e^(-bp)
e=p/Ae^(-bp)*{A*-b*e^(-bp)}
e= -pb

Answer 6

Revenue(r) =pq
r=p*Ae^(−bp)
dr/dp=Ae^(−bp)-pAbe^(−bp)
dr/dp=Ae^(−bp)*{1-pb)
for max revenue
dr/dp=0
gives1-pb=0
gives p=1/b

unite price that maximises revenue=1/b
note that at this point |e|=1