Question

2) Suppose that Scott and Bob live on the same street. In the winter, both of them like their streets plowed. Bob's demand is given by Q = 40 – P, and Scott's demand is given by Q = 30 – 2P. Suppose that the marginal cost of plowing the snow is constant at $35.


(a) What is the social marginal benefit curve?


(b) What is the socially efficient amount of plowing that should be done?


(c) What would be the socially efficient amount of plowing if the marginal cost of plowing were $5?

Answer 1

A) SMB Curve is Vertical Summation of individual demand curve

P = 40-Q, P = 15-.5Q

If Q <= 30

So SMB: P = 55 - 1.5Q,

If Q> 30,

SMB: P = 40-Q

B) at eqm, SMB = PMC = 35

Then, 55-1.5Q = 35

20 = 1.5Q

Q* = 13.33

SMB Curve (13.33, 35) MC (30,10) 20 30 40

C) if MC = 5

Then Q's = 35

SMB Curve (13.33, 35) MC (30,10) \(35,5) 20 30 40