Question

Question 11

A. Suppose Scott and Bob live in the same street. In winter, both love when their streets are cleared of snow. Bob's snow removal request is given by Q = 40 - P, and Scott's request is given by Q = 30 - 2 P. Assume that the marginal cost of snow removal is constant at $ 35.

a) What is the social marginal benefit curve?

b) What is the amount of socially effective snow removal that should be done?

c) What would be the amount of socially effective snow removal that should be done if the marginal cost of snow removal was $ 5?

B. In a community, 20 people each have a demand Q = 20 - P for street lighting (Q is the number of street lighting units and P is the price per unit) and 5 other people have each a request Q = 18 - 2P for public lighting. The production cost of a public lighting unit is $ 10. Determine the number of socially optimal public lighting units (It is assumed that it is impossible to produce a fraction of a public lighting unit).

Answer 1

Scott's marginal benefit=Q= 30-2P or P= 15-0.5Q

Bob's Marginal benefit=Q=40-P or P= 40-Q

A. Social marginal benefit= Scott's marginal benefit+ Bob's Marginal benefit

P= 15-0.5Q+40-Q

P= 55-1.5Q

B. Socially effective snow removal:

55-1.5Q= 35

20/1.5=Q

Q*=13.33= Socially efficient amount

C. 55-1.5Q=5

50/1.5=Q

Q*= 33.33

B. Q=20-P

P= 20-Q

For 20 people, multiply it with 20

P= 400-20Q

Q=18-2P

P= 9-0.5Q

For 5 people multiply it with 5

P= 45-2.5Q

Total willingness to pay for 25 people=

400-20Q+45-2.5Q= 445-22.5Q

Socially optimal level

445-22.5Q=10

435/22.5= Q

Q*= 19.3 Street lights.

If it helps kindly upvote