Answer to Question #258706 in Economics of Enterprise for dab

Question

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 4-10 shows 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

Solution:

The supply and demand curves are as follows:

Using New Jersey as an example, the cigarette tax was raised from 40 cents to 80 cents, raising the price per pack from 2.80 cents. As a result, cigarette consumption dropped from 52 million packs to 47.5 million packs. The increase in the cigarette tax led to this decrease in consumption. So, what we're seeing is a perfectly elastic supply, which means that raising the cigarette tax from 40 cents to 80 cents will increase supply.

 

The price and revenue changes can be seen in the graph below. The initial equilibrium is located at E, and it has shifted to E₁.

 

 

Q = AP^-e

Ed = $\frac{\partial Q} {\partial P}\times \frac{P} {Q} = \frac{-4.5} {0.4} \times \frac{2.80} {47.5} = -11.25 \times0.06 = -0.675$

The value of e = -0.675

Substitute to derive A:

47.5 = A2.80^-0.675

A = 6.39