Can you calculate elasticity?
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.
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Verified answer
elasticity=%(change in quantity)/%(change in quantity)
when it comes to calculus
change in quantity=dq
change in price =dp
%change in quantity=100*(dq/q)
%change in price=100*(dp/p)
=>e=(100*dq/q)/100*(dp/p)
e=(dq/q)*(p/dp)
e=(dq/dp)*(p/q)
or e=p*d/dp(log q)
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
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
comparable form of elasticity. The arc elasticity is used whilst a function for the finished call for curve isn't standard, or no longer handy expressed as a carry out of fee and extensive style. The arc is only area of the curve between 2 components the placement we are able to compute this sort of the curve