The Economic Theory of Environmental Quality

    The material in this section can be rather rough going for non-economics majors.  We'll do what can be done to make it palatable!
    In economics, household decisionmakers are assumed to "maximize utility"--that is, they attempt to select the bundle of goods that they most prefer, given the constraints imposed by the prices they pay and the incomes that they possess.  Similarly, firm decisionmakers are assumed to "maximize profit"--that is, they attempt to make the difference between the revenue they receive and the costs they pay as large as possible.  [Note: for home production, these are the same].  Imagine two types of goods, Qp (a good that generates polluting residuals, R, in its consumption or production) and Qnp (a good that does not generate pollution).  Of course, the actual goods falling into each category will differ for the households and the firms (e.g. steel involves a lot of pollution, r, to produce, but not much to consume, while fireplace logs involve lots of pollution at the consumer level, but much less at the producer level).  For simplicity, we won't worry about that distinction  and we will assume that R is homogeneous (for the time being).  AND, to make things convenient, we'll count output in terms of tons (unusual, but doesn't affect anything if technology is given).
    The consumer, then, is trying to maximize:
        U = U(Qp, Qnp, Eo)
subject to: PpQp + PnpQnp = Y
where
    Qp = the good that involves pollution in its consumption
    Qnp= the good that does not involve pollution in its consumption
    Eo = the existing level of environmental quality, that the individual household is too small to have a noticeable effect on, but that collectively they determine (along with firms).
(Omitting some math),
the condition for this maximum is:    MUQp/Pp = MUQnp/Pnp   (intuition--suppose this condition did not hold; do some numbers)

BUT, the "price" being paid for Qp it too low by the amount of marginal damages, Pr, associated with each unit of R discharged (Qp=R for the consumer):  that is, the price of the polluting good "should" be (to cover full social costs) = Pp + Pr.  Hence, the household's optimum should be:     MUQp/(Pp + Pr) = MUQnp/Pnp.
IMPLICATION: Each household buys too much of the polluting good from society's perspective, implying that R is too large collectively.  Eo, then, is too low--since E = f(R)  that is (like in the 5-Box diagram), the residuals operating through a dispersion function determine environmental quality).

    The firm's situation is only a little more complicated.  The polluting good producer tries to maximize:
    Z = QpPp - PxX-PmM
where
    Z = profits
    Qp = quantity of the polluting good produced, measured in tons--this is a function of X, M.
    X = non-material inputs (labor and capital)
    M = polluting inputs (coal, taconite, etc--note that some of polluting inputs can go into the good and not enter the environment; that is, M = Qp + R for the firm--a ton of polluting input either goes into output or residuals from the Law of Conservation of Matter for ordinary production)
(Omitting some math),
the condition for this maximum is:  MBinput = MCinput for all inputs.  We need only look at what that means for each input (here we will assume a competitive industry in both input and output markets):
    MBinput = PpMPQp for any input (X or M), while
    MCinput = Pinput (Px or Pm)
Hence, considering our two inputs, we have that at a profit maximum
    PpMPx = Px   and
    PpMPm = Pm
Critical to understanding:  Qp = M - R  (that is, any material inputs, M, that don't come out of the plant as part of the final product must come out as residuals, R).  As with the consumer, the price of the materials input fails to capture the full cost of using them, because of the environmental damage their use entails.  The "correct" MB & MC conditions for the firm are, then:
    PpMPx = Px -PrMPx,   or, rewriting,  PpMPx +PrMPx = Px  or (Pp +Pr)MPx = Px  and
    PpMPm = Pm + Pr(1 - MPm)
[Look at implications--A) hiring too little X, since the MPx gets you benefits of not only the value of the output, Pp, but also the saving in charges for residuals, since any additional output due to X inputs reduces residuals, since we are holding constant materials inputs, M, in this equation; B) hiring too much M, because its true cost is greater than it appears in the uncontrolled case, and C) over-producing since the full costs of production are greater, when the cost of any input goes up (easy to prove, but not really appropriate for this class, and intuitively obvious--the marginal costs of production are higher with Pr than without; and (bringing A-C together) D) emitting too much R].

NOTE:   Eo = f(Rconsumer+Rfirm), and in uncontrolled case (Pr = 0), both households and firms emit too much residuals.  Hence Eo is too low from society's perspective.  If we set Pr = marginal social damages from residuals, then goods collectively will get more expensive but that will be offset by the gain in environmental quality, that is:

    U(Qp*, Qnp*, E*) > U(Qp, Qnp, Eo)     which just says that we get a "preferred bundle" containing the right amounts of environmental and non-environmental goods when we charge the socially-optimal price for emitting residuals (the marginal damage that those residuals do).

    NOTE:  It is not clear whether households or firms are "more responsible" for residuals and, hence, our environmental quality.  Automobile pollution is largely due to consumers, steel production largely due to producers.  BUT, it is not even clear that such a distinction makes any sense--the firms are in existence because they produce the goods we want...the only reason that their production occurs in "plants" and not in *our* homes is scale economies of production that makes the former a less expensive way to get the things we want.  It is really our behavior (wanting goods that involve pollution in their production) that is the ultimate source of the environmental quality we observe around us!  In a democratic society, we can set the rules by which the firms produce--but remember that if we set those rules "wrong" (e.g. by setting a Pr either too low or too high), it is us that we ultimately harm not the firms.  They will adjust, by reducing production, going out of business, changing methods of production, etc--but ultimately we are the ones experiencing the mix of ordinary and environmental goods that exist.