Question

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:

P2-P1
_________

(P2+P1)/2

I got some of the calulation:

Percentage change in P=

.20 Quantity/.4 Price Elasticity of Demand = 0.5

P2-2
_______ = 0.5

(P2+2)/2

I have tried the calculation several ways and I can not arrive at the answer of $3.33.

Answer 1

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