The total operating revenues of a public transportation authority are $100M while its total operatiing costs are $120M. The price per ride is $1, and the price elasticity of demand for transportation ia -0.4. The transportation authority has to eliminate its operating deficit.

(a)What pricing policy should the transportation authority adopt? Why?(b What price per ride must the public transportation authority charge to eliminate the deficit if it cannot reduce costs?
b) suggestion: increase the price of a ride to be $1.50

To determine the pricing policy and the price per ride required to eliminate the operating deficit, we need to understand the concept of price elasticity of demand and its relationship with revenue.

Price elasticity of demand measures the responsiveness of the quantity demanded to a change in price. In this case, the price elasticity of demand for transportation is given as -0.4, which means that a 1% increase in price will lead to a 0.4% decrease in the quantity demanded.

(a) What pricing policy should the transportation authority adopt? Why?

To eliminate the operating deficit, the transportation authority needs to generate more revenue. They can adopt different pricing policies, such as increasing the price per ride, introducing peak and off-peak pricing, or offering discounted passes or subscriptions.

Since the price elasticity of demand is negative (-0.4), we know that demand is relatively inelastic, meaning that a change in price will have a lesser impact on the quantity demanded. In this case, increasing the price per ride is a viable pricing policy.

(b) What price per ride must the public transportation authority charge to eliminate the deficit if it cannot reduce costs?

To calculate the price per ride required to eliminate the operating deficit, we need to consider the revenue and cost figures given. The operating deficit is the difference between the total operating costs ($120M) and the total operating revenues ($100M), which is $20M.

Let's assume the current number of rides is R, and the current price per ride is P ($1).

The current total revenue (TR) is given by: TR = R * P = 100M

The deficit can be represented as: Deficit = Total Costs - Total Revenue
Deficit = $120M - $100M
Deficit = $20M

To eliminate the deficit, the transportation authority needs to generate an additional $20M in revenue. They can achieve this by increasing the price per ride (P) while maintaining the same number of rides (R).
Let's calculate the increase in price required:

Deficit = Additional Revenue
$20M = (R * (P_new - P))

Since the price elasticity of demand is given as -0.4, we can use this information to estimate the approximate increase in price required:

-0.4 = [(R * (P_new - P)) / (R * P)]
-0.4 = (P_new - P) / P
-0.4P = P_new - P

Simplifying the equation:
-0.4P = P_new - P
0.6P = P_new

Therefore, the new price per ride required to eliminate the deficit is approximately 0.6 times the current price per ride. In this case, the current price per ride is $1, so the new price per ride would be 0.6 * $1 = $0.60.

However, it is important to note that this calculation assumes that demand remains constant after the price increase. If the price increase has a significant negative impact on ridership, the transportation authority might have to adjust its strategy accordingly.

In your suggested solution, increasing the price per ride to $1.50 can potentially generate additional revenue and help reduce the deficit. However, it is crucial to carefully monitor the impact on demand and adjust the pricing policy accordingly to strike a balance between revenue generation and ridership.