Question

Questions 1. (100) In a market for dry cleaning services, the marginal benefits from using dry cleaning services are MBp = 100-Q, and the private marginal cost of producing those dry cleaning services is given by MCp = 10 + Q. Pollution created by the dry cleaning process creates external damages that are given by the equation MCext = Q, giving social marginal costs of MCs = 10 + 20 (a) In the same graph, graph private and social marginal benefits and marginal costs (MB, MB, MCp, and MCs). Draw a fairly large graph. (b) Calculate the socially efficient allocation of the product, and label it with both symbols (Q.) and numbers in your graph for part a. (c) Calculate the privately efficient allocation of drying cleaning services, and label it with both symbols (g) and numbers in your graph for part a. (d) (i) In your graph for part a, shade in the area representing the change in social net benefits if o is allocated instead of o* (ii) Calculate the value of this change in social net benefits. (iii) Is this change a social gain or a social loss

i would really appreciate if any one could elobarote on question (d), i dont really understand how to find question (d). thanks

Answer 1

(a)

Using MBp function, when Q = 0, MBp = 100 (vertical intercept) and when MBp = 0, Q = 100 (horizontal intercept).

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

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

Graph of the functions as follows.

P, MB. ус 100 MB зо | 100 g

(b)

When outcome is Socially efficient, MBp = MCs.

100 - Q = 10 + 2Q

3Q = 90

Q = 30

P = 100 - 30 = 70

In above graph, efficient outcome is at point A where MB intersects MCs, with price Ps* (= 70) and output Qs* (= 30).

(c)

In market equilibrium outcome, MBp = MCp.

100 - Q = 10 + Q

2Q = 90

Q = 45

P = 100 - 45 = 55

In above graph, market equilibrium is at point B where MB intersects MCp, with price Pp* (= 55) and output Qp* (= 45).

(d)

(i) Change in social net benefits = Area of triangle ABC

(ii) If Q = 45, MC_ext = Q = 45

Change in social net benefits = (1/2) x MC_ext x (Qp* - Qs*) = (1/2) x 45 x (45 - 30) = (1/2) x 45 x 15 = 337.5

(iii) This Change in social net benefits is a social gain, if the external cost is internalized.