BUSI 300. Review and Discussion Answer Guide No. 8

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1 BUSI 300 Review and Discussion Answer Guide No. 8 CHAPTER 9: Transportation and Congestion 1. You should probably choose the central city property. In the short run, the imposition of tolls will increase the marginal cost of commuting, cause the housing price function to get steeper, and increase prices at all locations. With higher housing prices and commuting costs, utility in this city will be lower than utility elsewhere, and emigration will occur. Thus, in the long run, the city will shrink (the boundary will move inward) and the housing price function will shift downward. Prices near the edge of the city will fall. If there is a fixed factor that is less congested in the now smaller city, prices near the city centre will rise.

2 Guide 8 Page 2 of 5 2. The basic problem with capacity expansion is Down's law, or the law of highway congestion. Some drivers are discouraged from using congested highways precisely because they are congested. Capacity expansions may temporarily reduce congestion, but this will just encourage more people to drive. Thus, in the absence of road pricing, capacity expansion is self-defeating. There are well documented cases of an increase in capacity leading to an increase in traffic congestion. 3. (a) The total cost equals the private cost plus the external cost, so TC = 4 + 2V. (b) Equilibrium volume occurs where the demand and private cost curves intersect. P = PC implies 16 V = 4 + V implies V1 = 6. Optimum volume occurs where the demand and marginal cost curves intersect. P = MC implies 16 - V = 4 + 2V implies V2 = 4. The diagram should resemble the figure in Exercise 9.1, except that the PC and MC curves both have an intercept of 4 on the vertical axis. The MC curve is twice as steep. (c) The capacity of the road is actually 0 in this problem, and so there is congestion at the efficient traffic volume V2. (d) Each driver ignores the impact of his travel decision on others, and this negative externality leads to excessive road use. (e) The required toll equals EC at V2, or $4 per trip. In the diagram, this is the vertical distance between PC and MC at V2. 4. Answers will vary. Discuss with your classmates on the course discussion forum.

3 Guide 8 Page 3 of 5 5. (a) Drivers will travel right up to the point where the private costs meet but do not exceed the benefits of travel. To find equilibrium, set demand, which is representative of the benefits of travel, equal to the private costs of travel. Currently the demand curve is expressed as the number of trips as a function of the cost of travel: V = 100 2P Rearrange the demand curve so that it tells us the benefits of travel as a function of the number of trips, i.e., solve for P as follows: 2P + V = 100 2P = 100 V P = 50 $0.5V This tells us what the travel benefits are as a function of the number of trips. Now, set these benefits equal to the costs (assuming for now that there are no external costs, EC = 0, meaning the private costs are the total cost of travel): P = PC Set demand equal to private cost and solve for V: Demand: P = $50 $0.5V Private cost: PC = $V $50 $0.5V = $V Solve for V in this equation to find the equilibrium traffic volume. $50 $0.5V = $V $50 = 1.5V V = $50/1.5 V = = equilibrium traffic volume (b) Find the socially optimal traffic volume. This time, set the benefits equal to the total costs: P = PC + EC $50 $0.5V = $V +$V $50 $0.5V = $2V $50 = $2.5V V = $50/$2.5 V = 20 = socially optimal traffic volume (c) To find the toll that will induce the socially optimal traffic volume, find the difference between the personal cost and the total cost at the optimal level of traffic. We have an equation that describes the personal cost as a function of traffic volume: PC = V

4 Guide 8 Page 4 of 5 And we have a function that describes the total cost as a function of traffic volume: TC = PC + EC = 2V Thus, the toll is equal to: Toll = TC PC Toll = 2V V Toll = V So now plug the optimal traffic volume of 20 into the above equation: Toll = $20 The toll should be $20 in order to force drivers to internalize the negative externality they impose on others by joining the road, and induce the optimal traffic volume. Notice that this particular PC curve implies congestion costs for any level of traffic greater than zero, which implies that even at the socially optimal traffic volume there is some congestion (since the social optimum is not zero). Alternative Solution for Finding Equilibrium The solution presented above finds the equilibrium and optimum traffic volumes by first ensuring that all three equations have the price variable on the left hand side. That is a useful conceptual practice, but it is not the shortest route to a solution. Some students may find the following slightly more straightforward. First, recognize that we have an equation that specifies the demand for travel, or traffic volume, as long as we know the price. This is the demand curve, which is: V = $100 $2P.

5 Guide 8 Page 5 of 5 Next, we know that the private cost is equal to V, so we can find the equilibrium solution in which commuters only consider their private costs by plugging this value in for P in the demand equation. Thus: $V = $100 $2P $V = $100 2V $3V = $100 V = $100/$3 = = equilibrium traffic volume Similarly, to solve for the optimum traffic volume, start with the same demand curve $V = $100 $2P and replace P with the total cost of $2V. Thus: $V = $100 $2P becomes $V = $100 $2(2V) $V = $100 $4V $5V = $100 V = $100/$5 = 20 = optimal traffic volume