Given that a city has 120 commuters. Given inverse demand function for commuting on highway: D(T) = 120 ? T. This function means the marginal benefit (in dollars) of adding another car to the road when there are T cars on the road. If T people are using highway, travel times (in minutes) are M(T) = T. Everyone values their time at 2 dollars per minute.

a) Why might the marginal benefit of using the road differ across people?

b) Derive the social marginal cost curve. Please give steps in details.

c) When there is no toll, what are the equilibrium quantity of highway users, equilibrium quantity of alternative-route users, equilibrium total cost of commuting for highway users, equilibrium total cost of commuting for alternative-route users, equilibrium total cost of commuting? Show every step for computing all these quantities and show all these quantities' curves on a graph.

d) When the toll is set to maximize social welfare, what are the equilibrium quantity of highway users, equilibrium quantity of alternative-route users, equilibrium total cost of commuting for highway users, equilibrium total cost of commuting for alternative-route users, equilibrium total cost of commuting, toll and toll revenue? Show every step for computing all these quantities and show all these quantities' curves on a graph.

e) For each person, how much better or worse off they are after the introduction of the toll? Is there enough toll revenue to compensate for their loss in welfare?

Answer all the following questions Consider the bivariate random vector 1. Expand the matrix form of the density function to get the usual bivariate normal density involving 01, 02, p and exponential terms in (21 - (1)2, (11 -(2) and (12 -(2)2. 2. Explain what happens in the following scenarios: (a) p=0 (b) p = 1 (c) p= -1Moving to another question will save this response. Question 2 Which of the following statement about an annuity due is false? The first cash flow is made on the first day of agreement The last cash flow is made one period before the end of the agreement Cash flows occur at the beginning of each period The first cash flow is made one compounding period after the date of the agreement Moving to another question will save this response