Topics in Environmental and Natural Resource Economics

1
Topics in Environmental and Natural Resource
Economics

• Steven C. Hackett
• Professor of Economics
• Humboldt State University

2
Topics in the Theory of Environmental Controls

• Topic 1 Taxes v. Subsidies
• If we pay polluters a subsidy in return for them
  reducing their pollution emissions, will the
  subsidy be as efficient as the Pigouvian tax?
• Topic 2 Standards
• If regulators do not have enough information
  about marginal external costs to use Pigouvian
  taxes to internalize externalities, how effective
  are standards (quantity restrictions)?

3
Taxes vs. Subsidies

• Assumptions
• Firms in a polluting industry emit z units of
  pollution for each unit of output q, in fixed
  proportions (the firm can only reduce z by
  reducing q).
• The industry is otherwise assumed to be
  well-functioning and competitive.
• The regulator seeks the socially optimal level
  of pollution control (maximize total net benefits
  to society).

4
Taxes vs. Subsidies

• Case 1 Socially optimal pollution tax
• In the case of a tax, the regulator can impose a
  tax of t dollars per unit of pollution. t is
  equal to marginal external cost.
• Each firm is a price taker in the market where
  it sells its product, and thus sells each unit
  q at a constant price p.

5
Taxes vs. Subsidies

• Assumptions, continued
• The firms total cost of production is c(q),
  with c(q) denoting marginal cost (?c(q)/?q).
• Firms seek to maximize profit p
• ? pq c(q) - tzq

6
Taxes vs. Subsidies
The firm chooses q to maximize profit, which
occurs where ??/?q 0 (As a sidebar, note that
this is called a first-order necessary condition.
If ? is a twice continuously differentiable and
strictly concave function, then this first order
necessary condition is also sufficient in
identifying a unique maximum. Lets assume that
this condition holds.)
??/?q 0 ? p c(q) tz 0
Rearranging we get p c(q) tz
7
Taxes vs. Subsidies
p - tz c(q) Thus the firms profits are
maximized where the net price (p tz), the
sales price of each unit of output net of the
pollution tax on each unit sold equals marginal
private cost c(q).
8
Taxes vs. Subsidies
(p tz) is the marginal value (or benefit) that
society assigns to a unit of the product made by
the firm. Note that total net benefits to
society are maximized when marginal benefit
marginal cost. Thus the Pigouvian tax
internalizes the externality and maximizes net
benefits to society.
9
Taxes vs. Subsidies
Case 2 Subsidy to firms that reduce pollution
The regulator selects a total maximum allowable
quantity of pollution emissions Z. For example,
Z might be 10,000 pounds of emissions per year,
established as a fraction of the firms
historical emissions. Note This represents a
correction of an error in the Hartwick and
Olewiler text The firms actual emissions are
zq. The regulator offers to pay the firm a
subsidy s for each unit the firm reduces actual
emissions below the maximum allowable emissions.
10
Taxes vs. Subsidies
Case 2 Subsidy to firms that reduce pollution
Note that the regulator must set BOTH Z and s
in the subsidy system, whereas in the tax system
the regulator need only set the tax t (though
it must know marginal external cost).
11
Taxes vs. Subsidies
Case 2 Subsidy to firms that reduce pollution
If the firm does not reduce its emissions, then
the subsidy is an opportunity cost income that
the firm forgoes by not abating its emissions.
12
Taxes vs. Subsidies
Case 2 Subsidy to firms that reduce pollution
The firm maximizes profit ? ? pq c(q)
s(Z-zq) As before, assume that ? has the
concavity properties for a unique maximum to
occur where ??/?q 0.
13
Taxes vs. Subsidies
Case 2 Subsidy to firms that reduce pollution
? pq c(q) s(Z-zq) Note that if zq gt Z, and
emissions exceed the maximum allowed, then s
can be interpreted as a tax on the excess
emissions.
14
Taxes vs. Subsidies
Case 2 Subsidy to firms that reduce pollution
??/?q 0 ? p - sz c(q) On the left-hand side,
note that an incremental increase in q
increases revenues by p but reduces the amount
of the subsidy by sz.
15
Taxes vs. Subsidies
Case 2 Subsidy to firms that reduce pollution
??/?q 0 ? p - sz c(q) Thus profits are
maximized when price net of the forgone subsidy
equals marginal cost.
16
Taxes vs. Subsidies
Case 2 Subsidy to firms that reduce pollution
If s t, then the subsidy and the tax have the
exact same impact on the firms short run
quantity choice (the first-order conditions are
the same). Reducing quantity (and thus emissions)
by one unit saves the firm t dollars in the tax
system, or pays the firm s dollars in the
subsidy system.
17
Taxes vs. Subsidies
Taxes and subsidies have markedly different
long-run effects in the overall market,
however. In a long-run equilibrium in a
well-functioning competitive market, price per
unit is just sufficient to pay the average cost
to produce a unit of the good (p AC).
Economists call this zero economic profit.
18
Taxes vs. Subsidies
Positive economic profits attract entry by new
firms in the long run, driving price down, while
negative economic profits drive some firms to
exit the industry in the long run, driving price
up. The long-run equilibrium in a competitive
market must occur at zero profit, because only at
that point is price in equilibrium.
19
Taxes vs. Subsidies
Case 1 Tax The tax increases the firms marginal
cost and average cost. If the industry was in a
(zero profit) long-run equilibrium, then the tax
causes profits to become negative. In the
adjustment to a new long-run equilibrium some
firms must exit the industry. This causes the
supply curve to shift inwards, raising market
price and reducing market quantity.
20
Taxes vs. Subsidies
Case 2 Subsidy The subsidy increases the firms
marginal cost just like the tax producing
another unit of output entails more pollution
emissions and the opportunity cost of the
foregone subsidy. Thus the subsidy has the same
short-run effect as the tax in reducing the
firms output. Therefore in the short run the
tax and the subsidy reduce pollution
equivalently.
21
Taxes vs. Subsidies
Case 2 Subsidy The problem is that the subsidy
can generally be expected to decrease the firms
average cost. Why? If Z is set as a fraction of
past total emissions, then in general the firm
responds to the subsidy by reducing output
relative to the historical quantity that resulted
in Z units of total pollution.
22
Taxes vs. Subsidies
Case 2 Subsidy Reducing quantity relative to
historical levels causes zq lt Z, which in turn
results in the firm receiving a subsidy for
reducing output. Quantity is the same in the
short run as with the tax (when t s), but the
total cost of producing q is less with the
subsidy. Since AC TC/q, TC being lower ? AC is
lower.
23
Taxes vs. Subsidies
Case 2 Subsidy If, as in the case of the tax, we
assume the industry was in a (zero profit)
long-run equilibrium, then the subsidy causes
profits to become positive because p gt AC. In
the adjustment to a new long-run equilibrium some
new firms will enter the industry. This causes
the supply curve to shift outwards, reducing
market price and increasing market quantity.
24
Taxes vs. Subsidies
Subsidy causes supply, quantity, and thus
emissions to increase in the long run
Tax causes supply, quantity, and thus emissions
to decrease in the long run
Snew
Sold
p
p
Sold
Snew
D
D
q
q
25
Taxes vs. Subsidies
Therefore, while taxes and subsidies can produce
an equivalent marginal incentive to firms, and
thus have the same short-run effect, in the long
run at the scale of the overall market they
differ.
26
Taxes vs. Subsidies

• Taxes reduce aggregate pollution levels in the
  short run and in the long run by reducing the
  quantity of the good produced and sold (as we
  learned in the unit on Pigouvian taxes).
• Subsidies reduce aggregate pollution levels in
  the short run, but increase aggregate pollution
  levels in the long run due to entry by new firms,
  and failure to establish an industry-wide
  emissions cap.
• The long-run effect of the subsidy is thus
  counterproductive to the policy goal of reducing
  emissions.

27
Taxes vs. Subsidies

• Qualifications
• If we evaluate taxes and subsidies from a
  macroeconomic level rather than at the
  microeconomic level of the market, the
  distinction between the impacts of the two
  becomes muddied and more challenging to evaluate.
• The information requirements to set the tax and
  the subsidy based on marginal external cost are
  quite high.

28
Taxes vs. Standards Under Uncertainty

• Suppose that the firm knows its own marginal
  benefits (MB) function associated with its
  pollution emissions (i.e., cost savings from
  polluting). Note that marginal benefit refers to
  the change in total benefits caused by a small
  change in emissions (partial derivative).
• The regulator only knows the distribution of
  possible MB states for the firm, as well as the
  expected value of the firms MB from pollution.
  Thus the cost savings to the firm from polluting
  are uncertain to the regulator.

29
Taxes vs. Standards Under Uncertainty
The regulator is also assumed to know the
functional form for marginal damages (MD) to the
environment caused by the pollution.
Compare the use of a pollution tax t per unit
of emissions, and the use of a pollution standard
(total allowed emissions) Z. Note that if the
regulator knew marginal benefits and marginal
damages with certainty, it could use either a
standard or a tax to reduce emissions to the
socially optimal quantity.
30
Taxes vs. Standards Under Uncertainty
MD
/Z
t
tax
MB
Z
Standard (cap)
Pollution Z
31
Sidebar Benefit/Cost Analysis
Sidebar -- Background on benefit/cost analysis
Suppose that MB to the firm from polluting, and
MD to the environment and society, are both known
with certainty. If pollution is currently
unconstrained, then if we reduce emissions, at
what level of pollution z will net benefits to
society be maximized? Total Net Benefits Total
Benefits Total Damages We can find the maximum
of total benefits by setting the derivative of
total net benefits with respect to emissions z
equal to zero.
32
Sidebar Benefit/Cost Analysis
?TNB/?z 0 ? MB MD at z.
TNB
TNB
z
Pollution Z
33
Taxes vs. Standards Under Uncertainty

• Back to our point But what happens if the
  regulator is wrong about the firms MB curve? For
  example, suppose that the regulator overestimates
  MB.
• Case 1 Pollution standard Z (total allowed
  emissions)

Since the regulators overestimated the marginal
benefits to the firm from polluting, they set Z
(the allowed emissions) too high relative to Z,
the true socially optimal cap.
34
Taxes vs. Standards Under Uncertainty
/Z
MD
b
a
MB (estimated)
c
MB (actual)
Pollution Z
Z (std)
Z
35
Taxes vs. Standards Under Uncertainty
Area abc in the previous diagram illustrates the
deadweight social loss to society from the cap
being too high. Area abc is a deadweight loss to
society because it represents the amount by which
damages to the environment (and society) exceeds
the actual benefits to the firm from polluting,
for (Z-Z).
36
Taxes vs. Standards Under Uncertainty
Continue supposing that the regulator
overestimates MB. 2. Case 2 Pollution tax t
Since the regulators overestimated the marginal
benefits to the firm from polluting, they set t
(the pollution tax) too high relative to the tax
that would have cut emissions to Z, the socially
optimal quantity. The firm responds to tax t by
cutting emissions to Z, which is a bigger cut in
emissions than is socially optimal.
37
Taxes vs. Standards Under Uncertainty
/Z
MD
d
t
a
MB (estimated)
e
MB (actual)
Pollution Z
Z
Z
38
Taxes vs. Standards Under Uncertainty
Area dae in the previous diagram illustrates the
deadweight social loss to society from the tax
being too high. Area dae is a deadweight loss to
society because it represents the amount by which
benefits to the firm from polluting exceeds the
damages to the environment (and society) from
polluting, for (Z-Z).
39
Taxes vs. Standards Under Uncertainty
The reverse also holds. Note that if regulators
underestimate MB to the firm, as shown in the
Hartwick and Olewiler reading, then the standard
will result in too little pollution, and the tax
will result in too much pollution, relative to
the socially optimal.
If it is equally likely that the regulator will
under- or over-estimate MB to the firm, then
either regulatory scheme can result in more than
the socially optimal level of emissions.
40
Taxes vs. Standards Under Uncertainty
If regulators not only know the expected value of
the MB function, but also know the slope of the
MB curve relative to the MD curve, then the
regulator will know which regulatory scheme (tax
or standard) will generate the smaller deadweight
social loss.
41
Taxes vs. Standards Under Uncertainty
If the marginal damages curve (MD) is steeper
than the marginal benefits curve (MB) to the
firm, then the deadweight social loss from the
tax (area dae) is larger than the deadweight
social loss from the standard (area abc).
42
Taxes vs. Standards Under Uncertainty
/Z
MD
b
t
d
a
c
MB (estimated)
MB (actual)
e
Z (std)
Z
Z
Pollution Z
43
Taxes vs. Standards Under Uncertainty
If the marginal damages curve (MD) is flatter
than the marginal benefits curve (MB) to the
firm, then the deadweight social loss from the
tax (area dae) is smaller than the deadweight
social loss from the standard (area abc).
44
Taxes vs. Standards Under Uncertainty
/Z
MD
b
d
t
a
MB (estimated)
e
c
MB (actual)
Z (std)
Z
Z
Pollution Z
45
Taxes vs. Standards Under Uncertainty
What happens if the uncertainty is with regard to
the marginal damages curve (MD), and neither the
regulator nor the firm know the actual MD curve?
In the framework used here, there is no
difference in performance of the tax and the
standard. If the regulator sets t where
expected MD MB, the firm will set emissions at
Z, the same as the standard that the regulator
will set.
46
Excel Homework
Start a new sheet in your Econ 523 workbook
(labeled tx/sub/std). Let marginal benefits (MB)
to the firm from polluting be given by the
equation MB c - dZ, and let marginal damages
(MD) to the environment and society by given by
the equation MD a bZ. 1. For a 100, b
3, actual c 850, estimated c 1000, and
d 0.8, plot the curves in a fully labeled
chart. 2. Calculate the numerical value for area
abc and area dae (as illustrated in the preceding
slide show) and briefly (in words) explain the
economics of the relative efficiency properties
of taxes vs. standards in this case.
47
Excel Homework, Continued
3. Retain the parameter values for a and c,
but now suppose that b 0.8 and d 3.
Repeat the analysis done in preceding steps 1 and
2.