Question Three Consider two cities, A and B, which are joined by two routes, I and II, with one way roads only. There are 100 travellers who must travel from city A to city B. Route I links city A to city B through city C. This route begins with a road linking city A to city C, which has a cost-of-travel for each traveller equal to 0.5 + x/200, where x is the number of travellers on this road. Route I ends with a highway from city C to city B, which has a cost-of-travel for each traveller equal to 1 regardless of the number of travellers who will use it. Route Il links city A to city B through city D. This route begins with a highway linking city A to city D which has a cost-of-travel for each traveller equal to 1 regardless of the number of travellers who will use it. Route ll ends with a road linking city D to city B which has a cost-of- travel for each traveller equal to 0.5 + y/200, where y is the number of travellers on this road. i. Draw the network described above and label the edges with the cost-of-travel needed to move along the edge. [5 marks] ii. Travellers simultaneously choose which route to use. Find Ilash equilibrium values of x and y. [5 marks] iii. A change has been introduced to the road infrastructure by the government, who built a new (one-way) road from city C to city D. The cost-of-travel on this new road is 0. Find the Ilash equilibrium for the game played on this new road network. (5 marks] iv. How does the total cost-of-travel change, as a result of the new road from C to D? Justify your answer. [5 marks] After a while, the government decides to introduce an additional charge of 0.125 per user, to the users of road from city A to C, and reduce the charge for users of road from A to D by 0.125 per user. Find the new Ilash equilibrium. [5 marks]