T = TOR where To gives the congestion-free travel time and R gives the number of riders on the Bay Bridge. There are 100 workers, who choose between commuting on the Bay Bridge and working from home. The value of time is $20/hr. Absent commuting costs (i.e. when T = 0), everyone prefers working in the office. Denote a worker's willingness to pay to work in the office (instead of at home) when commute times are zero as Vo. To capture heterogeneity we assume each worker's Vo is drawn independently from a uniform distribution on the interval [0, o]. a) (10 pts) Derive the expected number of workers who commute to work in terms of o and To b) (10 pts) Derive the total expected consumer surplus associated with commuting over the Bay Bridge. c) (10 pts) Now suppose the government charges a fee of F to go over the bay bridge and that the proceeds of this fee are remitted to the entire population regardless of whether they drive or stay at home. Re-derive the expressions for the number of commuters and the expected total consumer surplus as a function of F. d) (10 pts) Now derive the optimal fee that maximizes total consumer surplus plus the total dollar value of the fee remittances. 3) Von thinking If tility