Answer
a) increase of 1.33
b) five years from now
c) One reason that teenagers might have a higher price elasticity is that they don't have as much of an income as adults.
Work Step by Step
a)
$Elasticity=\frac{(Q_{2}−Q_{1})/[(Q_{2}+Q_{1})/2]}{(P_{2}−P_{1})/[(P_{2}+P_{1})/2]}$
$40=\frac{(Q_{2}−Q_{1})/[(Q_{2}+Q_{1})/2]}{(P_{2}−2)/[(P_{2}+2)/2]}$
.4=change in Q/change in P
.4*change in P/.4 = change in Q/change in P * change in P/.4
change in P = change in Q/40
change in P = 20/40
change in P = .5
change in P = ${(P_{2}−P_{1})/[(P_{2}+P_{1})/2]}$
change in P = ${(P_{2}−2)/[(P_{2}+2)/2]}$
$.5 = {(P_{2}−2)/[(P_{2}+2)/2]}$
$.5*2= 2*{(P_{2}−2)/[(P_{2}+2)/2]}$
$1 = 2*{(P_{2}−2)/[(P_{2}+2)/2]}$
$1 = 2P_{2}-4 * 2/(P_{2}+2)$
$1 = (4P_{2}-8)/(P_{2}+2)$
$1*(P_{2}+2) = (4P_{2}-8)/(P_{2}+2)*(P_{2}+2)$
$P_{2}+2 = 4P_{2}-8$
$P_{2}+10 = 4P_{2}$
$10 = 3P_{2}$
$10/3 = 3P_{2}/3$
$3.33 = P_{2}$
$3.33-2=1.33$
b)
Since elasticity is usually larger in the long run, the policy will be more effective in five years than from one year from now. Also, since smoking is a difficult habit to quit, it might take some time for people to stop smoking.
c) Also, teenagers are not as addicted to smoking as adults are, so their demand is more elastic.
