Question

The Acmeville Metropolitan Bus Service currently charges $0.88 for an all-day ticket, and is used by an average of 433 riders a day. The bus company is not earning a profit, but according to their contract with the city, they cannot cut the number of buses on the road. They must therefore find a way to increase revenues. The bus company is considering increasing the ticket price to $0.99. The marketing department\'s studies indicate this price increase would reduce usage to 169 riders per day. Calculate the price elasticity of demand for bus tickets to determine if the bus company should increase price or decrease price to increase revenues.
Price elasticity of demand is? 7.45 I get but on the online hw, it says its wrong? I tried 7.5 too? I used the midpoint formula (q2-q1)/((q2+q1)/2) / (p2-p1)/((p2+p1)/2)

Answer 1

Answer:

Midpoint formula = - 7.43

Other formula = - 4.88

Elastic PED - Decrease price to increase total revenue

Explanation:

Price elasticity of demand is the responsiveness of quantity demanded to a change in price. The midpoint formula calculation is as follows:

(Q2 - Q1) / [(Q2 + Q1/2]

(P2 - P1) / [(P2 + P1/2]

In this scenario:

Q1 = 433 (old quantity)

Q2 = 169 (new quantity)

P1 = 0.88 (old price)

P2 = 0.99 (new price)

When this is substituted into the formula, it is as follows (I shall do it one step at a time to make it easier):

(169 - 433) / [(169 + 433/2]

(0.99 - 0.88) / [(0.99 + 0.88/2]

(169 - 433) / 301

(0.99 - 0.88) / 0.935

- 264 / 301

0.11 / 0.935

- 0.877

0.118

PED = - 7.43 (PED is always a negative figure because price and quantity demanded have an inverse relationship. i.e. when one falls, the other rises)

PED is elastic if it is more than 1 and elastic if it is less than 1.

In this case, 5.8 is more than 1, hence PED is elastic.

In such a case, a change in price will always lead to a higher change in quantity demanded. Therefore, it is important to decrease the price to increase total revenue.

However, a different answer can be obtained using a different PED calculation

% change in quantity demanded

% change in price

(Q2 - Q1) / Q1

(P2 - P1) / P1

(433 - 169) / 433

(0.99 - 0.88) / 0.88

0.61

0.125

PED = - 4.88