Question

Problem 1
There is no need for government intervention when positive externalities are present because no one is being harmed”. Discuss the validity of this statement.

Problem 2
Evaluate the following statement:
The only amount of acceptable pollution is no pollution at all

Problem 3

Following are marginal abatement costs of three firms, related to the quantity of emissions. Each firm is now emitting 10 tons/week, so total emissions are 30 tons/week. Suppose we wish to reduce total emissions by 50 percent, to 15 tons per week.
Compare the total costs of doing this:
(a) With an equiproportionate decrease in emissions
(b) With a decrease that meets the equimarginal principle

Emission (tons/week)	10	9	8	7	6	5	4	3	2	1	0
Firm 1 ($/ton)	0	4	8	12	16	20	24	28	36	46	58
Firm 2 ($/ton)	0	1	2	4	6	8	12	20	24	28	36
Firm 3 ($/ton)	0	1	2	3	4	5	6	7	8	9	10

Answer 1

Problem-1: When there are positive externalities a good is under-produced and under-comsumed in the free market, compared to optimal quantity of production/consumption. Therefore, a subsity may be given by the government to increase production and consumption of that good to optimal quantity; thus, increasing social benefit (welfare) by increasing production and consumption of a good with positive externality.

Problem-2: This statement is not correct. No pollution will also mean no production, if any production, however small causes some pollution. We need to compare costs and benefits of pollution and production/consumption. Costs of increased pollution need to be compared to benefits derived from production and consumption that is causing the pollution. When marginal cost of increased pollution are higher than marginal benefits of production/consumption, we need to lower pollution by lowering production/consumption. And, when marginal costs of increased pollution are lower than marginal benefits of production/consumption we can increase production to increase net benefit. Thus, optimal pollution is when marginal costs of pollution are equal to marginal benefits of production/consumption.

Part 3: a) Equiproportional decrease will require each firm to decrease by same proportion of 50% or 5 tons/week, from 10 tons/week to 5tons/week. The total costs for each firm will be:

Firm-1: 4+8+12+16+20 = 60

Firm-2: 1+2+4+6+8 = 21

Firm-3: 1+2+3+4+5 = 15

Total costs = 60+21+15 = $96 per week

b) Decreasing pollution with equimarginal principle requires that marginal costs of abatement need to be equated across firms, and firms that have lower marginal costs compared to others reduce pollution first.

Here we start by noting that 15 tons/week of total pollution needs to be reduced. Pollution will be reduced by firms that has the lowest marginal cost of doing so. First two tons are reduced by Firm 2 and Firm 3 at $1 per ton/week each. Third and fourth tons are reduced by Firm 2 and Firm 3 at $2 per ton/week. Fifth ton is reduced by Firm 3 at $3 per ton/week. And so on. We have to pick the lowest number in each row (firm with the lowest marginal cost of reducing pollution) until will reach a total of 15 ton/week reduction of pollution.

Total cost = 1+1+2+2+3+4+4+4+5+6+6+7+8+8+8+ = $69 per week

Thus, costs are lower by $96-$69, or 27$ per week using the equimarginal principal, compared to equiproportionate decrease.

Firms cost of reduction was as follows:

Firm-1: 4+8 = $12; educed 2 tons/week.

Firm-2: 1+2+4+6+8 = $21; reduces 5 tons/week.

Firm-3: 1+2+3+4+5+6+7+8 = $36; reduces 8 tons/week.