Hi there I need help with part f of this question.

1. The inverse demand for traveling on a given highway is D(4) = 100-q. This function tells us the marginal benefit (measured in dollars) of adding another vehicle to the road when there are already q vehicles on the road. (a) Why might the marginal benefit of using the road differ across people? If q people use the highway then travel times (measured in minutes) are T(4) = 20+ q/4. Everyone values their time at 50 cents per minute. (b) What is the total social cost (measured in dollars) of q people using the highway? (c) When there is no toll, what are the equilibrium * quantity of road users, per person travel time (minutes), . total travel time (minutes), per person cost (dollars), and * consumer surplus. (d) When the toll is set to maximize social welfare, what are the equilibrium * quantity of road users, * per person travel time (minutes), . total travel time (minutes), * per person cost (dollars), . toll, * toll revenue, and consumer surplus plus toll revenue. To solve for the optimal quantity of road users you can either use calculus or a spreadsheet (Excel/Google Sheets/etc). The optimal quantity of road users is an integer. There are two related approaches you can take. First, you can use the requirement that the social marginal cost equal the social marginal benefit (this is what was shown in the videos) or you can write down a (e) Who is hurt, who is better off? Specifically, can you tell me for each agent how much better or worse off they are? (f) When the toll is set to maximize profits (assuming there are no variable costs of tolling), what are the equilibrium BC0433 Problem Set 8 Page 2 of 2 quantity of road users, * per person travel time (minutes), . total travel time (minutes), * per person cost (dollars), * toll, * toll revenue, and consumer surplus plus toll revenue