(a) (10 pts) Calculate the social trip cost at each traffic volume and fill in t

Question

(a) (10 pts) Calculate the social trip cost at each traffic volume and fill in the blanks in the table.

(b) (5 pts) What is the equilibrium traffic volume?

(c) (5 pts) What is the socially optimal traffic volume?

(d) (10 pts) What is the appropriate congestion tax?

Traffic Volume Trip Time Per Driver (vehicles) (minutes) (minutes) (minutes)($) 100 200 300 400 500 600 700 800 900 Increase in Travel Time Total Travel External Private Social Marginal Time Trip Cost Trip Cost Trip Cost Benefit 12 12 12.6 14 16.2 19.2 23 27.6 0 0 3 7.2 13 20.4 29.4 40 52.2 3.2 3.2 3.26 3.4 3.62 3.92 4.3 4.76 5.3 3.2 3.2 3.56 4.12 4.92 5.95 7.24 8.76 10.52 (Demand) 22.12 19.64 17.16 14.68 12.2 9.72 7.24 4.76 2.28 0 0.01 0.018 0.026 0.034 0.042 0.05 0.058 0 0 0.3 0.72 1.3 2.04 2.94 5.22

Explanation / Answer

a)

Social trip cost = External Trip Cost + Private Trip Cost

b)

Equilibrium is when Marginal Benefit = Private Trip Cost and after that Marginal Benefit < Private Trip cost

Here, Marginal Benefit = Private Trip Cost = 4.76 when Traffic volume is 800

Therefore equilibrium is at 800 with private trip cost 4.76

c)

Socially optimal traffic volume is when Marginal Benefit = Social Trip Cost

Here, Marginal Benefit = Social Trip Cost = 7.24 when Traffic volume is 700

Therefore Socially optimal Traffic volume is at 700 with social trip cost 7.24

d)

Appropriate congestion tax = External Trip cost of socially optimum traffic volume

Here, External Trip cost of socially optimum traffic volume = 2.94

Therefore, Congestion Tax = 2.94

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