Question

. Suppose that Scott and Bob live on the same street. In the winter, both of them like the snow on their street to be 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. Using the inverse demand for each, solve for the social marginal benefit curve. b. What is the socially efficient amount of plowing? c. Suppose the input costs of plowing fell and marginal costs of plowing were now constant at $5

Answer 1

a. Using the inverse demand for each, solve for the social marginal benefit curve.

Bob: Scott:

Q = 40-P Q = 30 – P

(-1)Q – 40 = -P(-1) (-1)Q – 30 = -2P

40 – Q = P 30 – Q = 2P

((30 – Q) = 2P)/2

15 – 1/2Q = P

P = 15 – 1/2Q + 40 – Q

P = 55 – 1.5Q

Scott is no longer willing to pay anything when Q >30

Social Marginal Benefit curve: Q = 40 - P

b. What is the socially efficient amount of plowing?

SMB = SMC

35 = 55 – 1.5Q

Subtract from both sides and rearrange

1.5Q = 20

Q = 13.33

c. Suppose the input costs of plowing fell and marginal costs of plowing were now constant at $5.

55 – 1.5Q = 5

55-5 = 1.5Q

50 = 1.5Q

33.3 = Q*