Question 2: The level of fare evasion on Melbourne's public transport system has increased steadily in recent years. According to a report in The Age newspaper, fare evasion during the 2012-2013 financial year was 9.9% on metro trains, 11.9% on trams and 16% on buses.2 Suppose you are the director in charge of ticket inspections for Public Transport Victoria (PTV). You are worried that fare evasion is eroding the financial viability of the public transport system. As a result, you are debating whether or not to increase the number of ticket inspections on public transportation in order to lower fare evasion. At the moment you have enough resources to fund 4 inspections for every public transport route per day. To evaluate whether 4 inspections per route is the optimal number, consider the following model. Let the financial harm caused by fare evasion be represented by the function H(I), where the harm is a decreasing function of the number of inspections (I) per route per day. In particular, let H(I) = 225/I. On the other hand, the cost (C) of an additional inspection is equal to the wage and benefits that need to be provided to the inspector. Let this cost be as follows: C(I) = 251. == (a) Define the marginal benefit (MB) of additional inspections as the (instantaneous) reduction in financial harm. Write down an expression for this marginal benefit. What can you say about the relationship between the number of inspections and the marginal benefit? Provide some economic intuition for this. (b) Write down an expression for the marginal cost (MC) of an additional inspection. Define the total loss to PTV from fare evasion (L) as follows: L(I)=H(I) + C(I) (1) (c) Use equation (1) to solve for the optimal number of inspections, I*, per route per day. Show that, at this optimum value, it is the case that MB = MC. Use this equality to explain the trade-off you face in your decision to add more inspections. (d) Use your answers above to explain why 4 inspections per route per day is not the optimal choice for PTV.