A bridge connecting an island city to the mainland is operated by the local authority. Before the pandemic, the bridge usage was 200,000 trips a week, and the toll price was $6 per trip. The bridge is large enough that it never experiences congestion at this level of usage. The maintenance cost of the bridge is $62.4 million a year, or $1.2 million a week,independently of how many vehicles use the bridge. There is no cost to the local authority from allowing an additional vehicle to travel through the bridge.

Possibly due to the pandemic, demand for trips on the bridge has fallen to 150,000 a week. Concerned that they would be unable to cover the cost of maintaining the bridge at this lower level of usage, the local authority decides to divide the cost by the usage to come up with a new toll price of $8 per trip. At this new price, usage drops further, to 120,000 trips per week. In response, the authority raises the price to $10 per trip. This causes a further decline in bridge usage to 90,000 trips per week.

Assume the goal of the local authority is to maximize the profit and/or minimize the loss from operating the bridge, and consider the following questions.

a) Calculate the optimal toll price. Explain your reasoning.