Question

1. (100) In a market for dry cleaning services, the marginal benefits from using dry cleaning services are ??( = 100 − ?, and the private marginal cost of producing those dry cleaning services is given by ??( = 10 + ?. Pollution created by the dry cleaning process creates external damages that are given by the equation ??-./ = ?, giving social marginal costs of ??0 = 10+2?.

(a) In the same graph, graph private and social marginal benefits and marginal costs (MBp, MBs, MCp, and MCs). Draw a fairly large graph.

2. (b) Calculatethesociallyefficientallocationoftheproduct,andlabelitwithbothsymbols ( Qs* ) and numbers in your graph for part a.

3. (c) Calculate the privately efficient allocation of drying cleaning services, and label it with both symbols ( Q *p ) and numbers in your graph for part a.

4. (d) (i)Inyourgraphforparta,shadeinthearearepresentingthechangeinsocialnet benefits if Qs* is allocated instead of Q*p . (ii) Calculate the value of this change in

   social net benefits. (iii) Is this change a social gain or a social loss

Answer 1

(a)

From MB function, when Q = 0, MB = 100 (vertical intercept) and when MB = 0, Q = 100 (horizontal intercept).

From MCp function, when Q = 0, MCp = 10 (vertical intercept)

From MCs function, when Q = 0, MCs = 10 (vertical intercept).

P, MB. ус 100 MB зо | 100 g

(b)

Socially efficient outcome is obtained by equating MB and MCs.

100 - Q = 10 + 2Q

3Q = 90

Q = 30

P = 100 - 30 = 70

Socially efficient outcome is at point A where MB and MCs intersect with price Ps* (= 70) and quantity Qs* (= 30).

(c)

Private outcome is obtained by equating MB and MCp.

100 - Q = 10 + Q

2Q = 90

Q = 45

P = 100 - 45 = 55

Private outcome is at point B where MB and MCp intersect with price Pp* (= 55) and quantity Qp* (= 45).

(d)

(i) Change in social net benefits = Area ABC

(ii) When Q = 45, External cost = Q = 45

Change in social net benefits = (1/2) x External cost x Change in Q = (1/2) x 45 x (45 - 30) = (1/2) x 45 x 15 = 337.5

(iii) If this externality is internalized by producing efficient output, this is a social gain.