Environmental Economics 4th Canadian Edition By Barry C Field – Test Bank

When no threshold exists, the very first unit of emissions has an impact on the environment.

Positive economics studies “what is” by describing or explaining events that actually occur in the real world. An example of positive economics is the analysis of market data on actual prices and sales volumes of a particular good (many other examples are possible here). Normative economics studies “what ought to be” such as what the outcome of the economy or public policy ought to be in order to satisfy a certain goal (eg., fairness, social efficiency, etc.). An example of normative economics is designing an environmental policy that treats people of different income levels fairly (again numerous other examples are possible).

The diagram below shows the function described by: MAC = 100 – 2E.

To find the level of uncontrolled emissions, set MAC = 0 and solve for E:
0 = 100 – 2E
E = 100/2 = 50
To find the MAC of the 40^th unit of abatement, we first need to determine the level of emissions associated with this amount of abatement. Current emissions will equal uncontrolled emissions minus the level of abatement:
E = 50 – 40 = 10 units of emissions remaining
Now solve for MAC by substituting E = 10 into the MAC equation:
MAC = 100 – 2(10) = $80.
The TAC of 40 units of abatement will equal the area under the MAC from E = 10 to E = 50 which is the area of a triangle with height 80 and width of 40 (area A in the diagram below):
TAC = ½(80 × 40) = $1,600

The diagram below shows the function described by: MAC = 90 – 3E.

To find the level of uncontrolled emissions, set MAC = 0 and solve for E:
0 = 90 – 3E
E = 90/3 = 30
To find the MAC of the 10^th unit of abatement, we first need to determine the level of emissions associated with this amount of abatement. Current emissions will equal uncontrolled emissions minus the level of abatement:
E = 30 – 10 = 20 units of emissions remaining
Now solve for MAC by substituting E = 20 into the MAC equation:
MAC = 90 – 3(20) = $30.
The TAC of 10 units of abatement will equal the area under the MAC from E = 20 to E = 30 which is the area of a triangle with height 30 and width of 10 (area A in the diagram below):
TAC = ½(30 × 10) = $150

The following table summarizes the abatement that will take place at each MAC level and the total for each MAC level.

The first panel shows the individual sources’ MAC curves. Source 1’s MAC is represented by the blue line and Source 2’s MAC is represented by the red line. The second panel shows the aggregate MAC curve (the green line). Note the kink at MAC = $50.

The socially efficient level of emissions can be found where the marginal damage cost equals the marginal abatement cost. Set the two equations equal to solve for E*:

200 + E = 900 – 0.75E
1.75E = 700
E = 700/1.75 = 400 = E*
The socially efficient level of emissions is equal to 400 units.

The socially efficient level of abatement is found by subtracting the socially efficient level of emissions from the level of uncontrolled emissions. Uncontrolled emissions can be found where MAC = 0:

0 = 900 – 0.75E
E₀ = 900/0.75 = 1,200
A* = E₀ – E* = 1,200 – 400 = 800 units
The socially efficient level of abatement is equal to 800 units.

The total damage cost when emissions equals 400 units is the area under the marginal damage cost curve. When E = 400, MDC = 200 + E = 600. The area under the MDC curve will be the area of a rectangle with height of 200 and width of 400 and a triangle with height of 400 and a width of 400 yielding:

TDC = 200 × 400 + ½ (400 × 400) = 80,000 + 80,000 = $160,000.
The total damage cost at the socially efficient level of emissions is $160,000.

The total abatement cost at the socially efficient level of emissions is equal to the area under the marginal abatement cost curve from emissions of 400 to emissions of 1,200 (this distance represents the abatement of 800 units). When emissions are 400, MAC = 900 – 0.75(400) = 600. Total abatement cost is going to be the area of a triangle with height of 600 and base of 800:

TAC = ½ (800 × 600) = $240,000
The total abatement cost at the socially efficient level of emissions is $240,000.

The total social cost at the socially efficient level of emissions is equal to the sum of the TDC and the TAC:

TSC = 160,000 + 240,000 = $400,000
The total social cost at the socially efficient level of emissions is $400,000. At any other level of emissions, the TSC will be higher than the TSC at the social optimum.