Question

24. The corner gas station sells cigarettes, facing a linear downward sloping demand curve. To maximize
revenue, the manager set the price equal to 20 dollars and sold a quantity of 25 packs per day on
average. But to discourage smoking, the government just set a per-pack tax of 3 dollars, to be paid by
the buyer. Now, to maximize revenue, the manager will reduce quantity by [ Answer24 ] packs per
day on average.

Answer 1

Solution:

In case of linear downward sloping demand curve, revenue is maximized at mid-point of the demand curve, where price elasticity of demand is 1 (in absolute terms). With a per-pack tax of $3, percentage change in price = (change in price/initial price)*100 = (3/20)*100 = 15%

To keep the revenue maximized, percentage change in quantity demanded/percentage change in price = -1

Percentage change in quantity demanded = -1*15 = -15%

Percentage change in quantity demanded can be found as: (change in quantity demanded/inital quantity demanded)*100

(Change in quantity demanded/25)*100 = -15

Change in quantity demanded = -15*25/100 = -3.75

Thus, in order to maximize revenue, the manager will reduce quantity by 3.75 packs of cigarettes.