MicroeconomicsAlgebra Calculation
posted by GG on .
Consider public policy aimed at smoking.
Studies indicate that the price elasticity of demand for cigarettes in about 0.4. If a pack of cirarettes currently costs $2 and the government wants to reduce smoking by 20 percent, by how much should the govenment increase the price?
Answer in suppose to be $3.33. When I try to calculate using formulate I can not get the answer.
Formula is:
P2P1
_________
(P2+P1)/2
I got some of the calulation:
Percentage change in P=
.20 Quantity/.4 Price Elasticity of Demand = 0.5
P22
_______ = 0.5
(P2+2)/2
I have tried the calculation several ways and I can not arrive at the answer of $3.33.

You are very close. Check your arithmatic.
To avoid confusion, I will use Pn to mean P2 (price in period 2)
You have, as stated (Pn  2)/((Pn + 2)/2) = 0.5 So, solve for Pn.
First multiply numerator and denominator by 2/2 (=1). You get:
(2Pn  4) / (Pn + 2) = 0.5
Now multiply through by the denominator. You get:
2Pn  4 = .5Pn + 1
Move the Pn's to the left of the =, the constants to the right. so:
1.5Pn = 5
Divide both sides by 1.5:
Pn = 3.3333
QED