Question

10. Review the example of the New Jersey cigarette tax (p. 71). Using graph paper or a computer, draw supply and demand curves that will yield the prices and quantities before and after the tax. (Figure 4 -10shows the example for a gasoline tax.) For this example, assume
that the supply curve is perfectly elastic. [Extra credit:A demand curve with constant price elasticity takes
the form Y=AP e, where Y is quantity demanded, P is price, A is a scaling constant, and e is the (absolute value) of the price elasticity. Solve for the values of A and e which will give the correct demand curve for the prices and quantities in the New Jersey example.]

Answer 1

putting the given scenario in consideration, the tax on cigarette consumptionhas been doubled by the NJ state hence the price has increased to $2.80 from $2.40. Consequently, comsumption has declined due to income effect from 52 million to 47.5 million packs. The graph below shows the change in equilibrium

The initial Equilibrium is at E and it shifted to E'

Considering the scenario, the supply curve is anticipated to shift upwards 40 cents with thge assumption that it is perfectly elastic. Thi can be illustrated as shown in the figure below

After the equilibrium change, the market change situation is as shown below

The extra credit section states that the demand curve is of the form

$Y=AP^{-e}$

Before tax y=52 millio, P=240, so; $52\times10^6=A2.40^{-e}.......(1)$

After tax, Y=47.5 million, P=2.80, so; $47.5\times10^6=A.2.80^{-e}..............(2)$

Taking $\frac{1}{2}$

$\frac{52\times 10^6}{47.5\times 10^6}=\frac{A2.40^{-e}}{A2.80^{-e}}$

$1.09=\frac{2.40{-e}}{2.80^{-e}}$

$\therefore1.09\times2.80^{-e}=2.40^{-e}$

The A's on the top and bottom of the fraction cancel

Taking natural logarithms on both sides

$In(1.09\times 2.80^{-e})=In 2.40^{-e}\\0.091=0.15e\\\therefore e=0.59$

putting $e=0.59$ into (1)

$52\times10^6=A2.40^{-0.59}$

$A=\frac{52\times10^6}{2.40^{-0.59}}=8.7\times 10^7$

A demand curve with constant price elasticity that yields the prices and quantities before and after tax will be of the form

$Y=8.7\times10^7P^{-0.59}$

This can be illustrated as shown below

The graphy below shows constant elasticity