4. A bridge connecting an island city to the mainland is operated by the local authority. Before the pandemic, bridge usage was 200,000 trips a week, and the toll price was S6 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. Assume the goal of the local authority is to maximize the profit and/or minimize the loss from operating the bridge. Due to the pandemic encouraging more people to work from home (WFH) or move away and thus reducing demand for travel at all prices, weekly bridge crossings fall to 150,000. (Assume demand shifted in by the number of former commuters who now WFH or moved away). 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 a 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. a) Calculate the optimal toll price. Explain your reasoning. b) Suppose the local authority's Department of Transportation were revamped and its new staff could bring down the cost of maintaining the bridge to $52 million a year, or $1 million a week. What would be the new optimal toll price? c) Comment on the local authority's previous decision to set the original, pre-pandemic toll price at S6 per trip (when that price led to 200,000 trips per week). Was it optimal? If so, why? If not, explain whether the price should have likely been set lower or higher. If you believe there is not enough information to decide either way, explain what data you would require and why