Question

A firm will release 10 emission units into the environment if it does not take any action. It can control its emissions at the following costs: C(a)=12a2, where a is the firm’s abatement level. That is, the firm emits 10−a emission units after abatement. The firm faces an emission tax of t=4 per emission unit released in the environment.

a) Calculate the optimal abatement level of the firm. Also, calculate the resulting tax payments for the remaining emissions, the abatement costs, and the firm’s total costs (consisting of tax payments and abatement costs). Explain your results, and use a diagram to illustrate them.

b) Suppose that the firm can adopt a new technology. Adopting this new technology incurs fixed costs of 6 to the firm. With this new technology, the firm could then control its emissions at the following costs:

Cnew(a)=14a2.

What would be the optimal abatement level if the firm adopted the new technology? What would be the resulting total costs (which includes the fixed costs of adopting the new technology, the tax payments for the remaining emissions, and the abatement costs). Compare the costs in part a) and b). Should the firm adopt the new technology? Explain your conclusions, and use again a diagram to illustrate them.

c) Suppose there is no emission tax. Instead, the government imposes an emission standard that allows the firm to emit up to 6 emissions units, but not more. That is, the firm must abate 4 emission units. Should the firm adopt the new technology under these circumstances? Compare your conclusions with those in part b) and carefully explain the differences between part b) and part c).

Answer 1

Trade-off between Market Goods and Environmental Quality
Production possibility frontier of two goods: market goods and environmental quality (draw a PPF)
The more the production of market goods, the lower the environmental quality, given a state of technical know-how
Values placed by a society on environmental quality and on market goods (the social indifference curve, derived from social welfare function) determine the choice of the society where to locate on the PPF
Value of environmental quality vis-a-vis market goods may differ among societies according to educational level, income, and information.
A short-run choice can affect long-run choices between environmental quality and market goods
Excessive emphasis to market goods in the short run may damage the assimilative capacity of the environment and thus future productive capability of an economy (this shifts the PPF inwards).
Linkage Between Economy and Environment
Draw a box diagram to show linkages between Nature and economy.
Nature provides raw materials and energy to the economy. Economy uses the resources to produce goods that are then consumed. During production and consumption processes, residuals are emitted to Nature.
Environmental economics is the study of the flow of residuals (see the box diagram) and its impact in the natural world.
According to the First Law of Thermodynamics (also known as the Law of Conservation of Matters), matters only change in shape, size, or phases, the total weight is conserved. What goes in must come out. Thus, the total weight of raw material and energy inputs to economy must be balanced by the total amount of residuals flowing to the environment.
Simple Model of Pollution Control
Marginal Damage Function (MD)
Pollution causes many types of damages. The benefit of pollution control is a reduction in damages of lives and properties.
Let us define marginal damage. Marginal damage is the additional damage caused by an additional unit of emission.
Example:
If total damages increase from $30,000 to $35,000 when emissions increase from 10 tons per week to 12 tons per week, marginal damage is $2,500 per ton. [($35,000-$30,000)/(12 tons-10 tons)]=$2,500 per ton.
Marginal damage function is a relationship between quantity of emissions and the damage caused by emissions. Draw an upward-sloping marginal damage curve.
The curve assumes that marginal damage increases with increasing emissions.
There is a threshold below which marginal damage is zero.
The area below the function measures total damage.
Marginal damage is a time-specific function; it may shift with time because of changes in natural environment.
Let us focus on marginal damage from a non-cumulative pollutant (a pollutant which does not accumulate over time).
The marginal damage function is a population-specific function; it may shift with an increase in the number of people exposed to the pollutants.
Marginal Abatement Cost Function (MAC)
This function denotes the additional cost of achieving one more unit decrease in level of emissions.