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On a sunny day it is possible to rent a bicycle from one of the many rental firms in the city for use on the walkways along Boathouse Row in Fairmount Park.  The market for such rental is described by the following pair of equations:

P = 5 + 0.1 Q Supply

P = 20 - 0.2 Q Demand

1. In the boxes to the right of the equations indicate which is the supply curve and which is the demand curve for rentals.

2. What are the equilibrium price and quantity for bicycle rentals?

Price =    Quantity =

5+.1Q= 20 - .2Q

Q = 50 ==> P = 10

3. At the equilibrium what is apparent consumer surplus?

CS = 1/2 (20-10)(50) = 250

4. At the equilibrium what is apparent producer surplus?

PS = 1/2 (10-5)(50) = 125

5. What is the amount of apparent total economic surplus?

250+125 = 375

6. It is now recognized that the walkways are used by pedestrians as well as cyclists.  People on foot must maintain a constant vigil for maniacal cyclists on sunny days.  This vigilance is a negative externality and imposes a cost on pedestrians of $3 per cyclist.  What price and quantity are socially optimal when the cost of the externality is recognized?

Price = Quantity =

(5+3)+.1Q = 20 - .2Q

Q = 40 and P = 12

7. What is the marginal social cost of the last bicycle rental at the quantity you found in your answer to question 2?

MSC = 8 + .1(50) = 13

8. What is the private marginal cost of the last bicycle rental at the quantity you found in your answer to question 2?

Same as equilibrium price.  10

9.  What is the deadweight loss resulting from the negative externality imposed by cyclists on those on foot?

DWL = 1/2 (13-10)(10) = 15

10. How large a tax on bicycle rentals would be necessary to correct the problem of the externality?

$3

11. After the tax what number of bicycles will be rented?

Same as your answer in 6, Namely 40.

12. After the tax what is the price of a rental to the consumer?

$12

13. Net of the tax, what is the price received by bicycle rental companies?

$9

14. How much tax revenue is collected?

Tax revenue = 3(40) = 120

15. When the externality tax is imposed what is the amount of consumer surplus?

CS = 1/2 (20-12)(40) = 160

16. When the externality tax is imposed what is the amount of producer surplus?

PS = 1/2 (9-5)(40) = 80

17. What is the amount of total economic surplus when there is an externality tax?

Total = 240.

Note that Tax + CS + PS = 120 + 160 + 80 = 360.  If we add in the DWL from the tax then the total is 375. 

18. The tax revenue collected represents (check all that apply):
      the cost of the externality to cyclists
      the cost of the externality to pedestrians This is the only correct answer.  The taxes paid by cyclists and the rental company represent compensation paid to those who incur the cost of vigilance, although we haven't discussed how this transfer is affected..
      the cost of the externality to bicycle rental companies
      the cost of the externality to the local government