[Econ 8852](
[Prof. Richard L. Sweeney](

[(print this presentation)](


Environmental Economics Theory

Environmental economics is essentially the study of externalities

An externality is something that enters into the utility (or production) function of one agent but is chosen by another agent.
Classic example is something that enters directly:

Externalities can also enter indirectly/ alter consumption sets

However an important distinction is made between those cases and situations where the actions by one agent affect another’s utility through prices (a pecuniary externality)

Another classic example is the case of mutually beneficial production externalities

Meade (1952) considered the case of a beekeeper and nearby orchard.

A formal model of production externalities

from Phaneuf and Requate


[familiar FOCs below]

Find Pareto optimal allocation by maximizing $U_1$, holding $U_2$ at some reference level

\[\begin{aligned} Max_{x,z,l,E} & \hspace{5pt} U_1(x_1,z_1,E) + \lambda_u [U_2(x_2,z_2,E) - \bar{u_2}] \\ & + \lambda_x[f(l_x,E)- x_1 - x_2] + \lambda_z[g(l_z)- z_1 - z_2] \\ & + \lambda_l[l - l_x - l_z] \end{aligned}\]

Efficiency in consumption

Marginal rate of substitution equal for both individuals

\[\frac{\partial U_1()/\partial x_1}{\partial U_1()/\partial z_1} = \frac{\lambda_x}{\lambda_z} = \frac{\partial U_2()/\partial x_2}{\partial U_2()/\partial z_2}\]

Marginal product of labor equal to the shadow value on labor constraint in both markets

\[\lambda_x \frac{\partial f()}{\partial l_x} = \lambda_l = \lambda_z \frac{\partial g()}{\partial l_z}\]

Exchange efficiency sets slope of production possibility curve equal to slope of each individual’s indifference curve

\[\frac{\partial U_i()/\partial x_i}{\partial U_i()/\partial z_i} = \frac{\lambda_x}{\lambda_z} = \frac{\partial g()/\partial l_z}{\partial f()/\partial l_x}\]

Now look at the optimality condition for emissions

Reducing $E$ increase utility for both people directly, but decreases their utility indirectly by reducing $x$ consumed.

Taking the FOC wrt $E$, and rearranging yields

\[- \left[ \frac{\partial U_1()/\partial E}{\partial U_1()/\partial x_1} + \frac{\partial U_2()/\partial E}{\partial U_2()/\partial x_2} \right] = \frac{\partial f()}{\partial E}\]

Optimal $E$ equates the sum of each individuals marginal willingness to tradeoff $E$ for $x$ with the physical reduction in $x$ production induced by changing $E$

We can then compare this Pareto outcome to the competitive market

Individuals max \(Max_{x_i,z_i} \hspace{5pt} U_i(x_i,z_i,E) + \lambda_i[y_i - p_x x_i - p_z z_i]\)

Firms producing $x$ and $z$ max \(Max_{l_x,E} \hspace{5pt} p_x f(l_x,E) - w l_x\)

\[Max_{l_z} \hspace{5pt} p_z g(l_z) - wl_z\]

While the efficiency in labor use and exchange conditions are met, the emission allocation is no longer efficient

\[p_x \frac{\partial f()}{\partial l_x } = w\] \[p_x \frac{\partial f()}{\partial E } = 0\]

Firms face zero marginal cost of $E$ and use too much of it.

Pigou (1920) noted that optimality could be restored with a tax

Pareto: \(- \left[ \frac{\partial U_1()/\partial E}{\partial U_1()/\partial x_1} + \frac{\partial U_2()/\partial E}{\partial U_2()/\partial x_2} \right] = \frac{\partial f()}{\partial E}\) Consider tax $\tau$, so \(\pi = p_x f(l_x,E) - w l_x - \tau E\)

Pigouvian tax: \(\tau = -p_x \bigg[ \frac{\partial U_1()/\partial E}{\partial U_1()/\partial x_1} + \frac{\partial U_2()/\partial E}{\partial U_2()/\partial x_2} \bigg]\)

Coase (1960) challenged whether this was actually necessary



Efficiency restored by taxing baker at dentists marginal harm from vibrations.

Coase’s challenge

Colloquial conclusion:

Coase Theorem requires three assumptions

  1. Well defined property rights
  2. No transaction costs
  3. No income / endowment effects

These conditions (mainly 2) rarely satisfied in the real world

More recently, Myerson-Satterthwaite theorem casts further doubt on viability of property rights alone to efficiently adjudicate externalities

Other policy options

Most environmental regulations are not Pigouvian taxes, but “command and control”.

A simpler model

Household utility: $U_i(y_i,E)= y_i - D_i(E)$

Summing over $i$ yields the damage function: $D(E)=\sum_i D_i(E)$

Firms can abatement emissions at cost $C_j(e_j)$

Social net benefits of pollution = $\sum_j C_j(e_j) - D(E)$

Efficient allocation equates marginal damages with marginal abatement costs at all firms

\[C'_j(e_j) = D'(E) \hspace{15pt} \forall j=1,..J\]

Therefore, the marginal cost of each polluter are also equal

\[C'_j(e_j) = C'_k(e_k) \hspace{15pt} \forall j,k\]

This is a necessary and sufficient condition for cost-minimization of any policy (such policies are “cost effective”)

Pigovian taxes achieve this by construction: \(C'_j(e_j) = \tau \hspace{15pt} \forall j=1,..J\)

Regulation unlikely to be cost effective in practice

More importantly, regulator doesn’t actually know $C$

Another option: Cap-and-trade

Firm’s minimize total compliance costs:

\(TC_j(e_j) = C_j(e_j) - \rho e_j\) \(s.t. \sum_j e_j \leq \bar{Q}\)

Assuming firms are price takers,

\[C'_j(e_j) = \rho \hspace{15pt} \forall j=1,..J\]

Prices vs Quantities

In static world of full information (ie known MC and MD), taxes and allowances are equivalent

Weitzman (1974) considered efficiency when there is uncertainty about the damage or cost functions.

Prices vs Quantities: Steep MC


Prices vs Quantities: Steep MB


Summary of results: the Weitzman Rule

Intuition: Gradient tells you how bad it is to be wrong in each direction.

Intuition: pollution chosen by firms setting $MC = \tau$ or $\rho$. If costs don’t change, resulting marginal prices don’t change, and expected $E$ obtained.

Stavins 1996 considers correlated uncertainty.

Seems likely that uncertainty in MB and MC are positively correlated.

If that’s the case, quantity instrument becomes more appealing (can see this visually)

Roberts and Spence (1976) show a hybrid instrument can outperform either


Most recent cap-and-trade policies have included a price bounds

What is the active research in this area?

Probably the largest area of research involves estimating costs and benefits

Where possible economists still prefer to use revealed preference methods

As opposed to benefit transfer to assign value.

We’ll spend a week on the workhorse model in this area: hedonic property valuation.

  1. Great example of reduced form vs structural approach to EE
  2. Interesting overlap with behavioral

This course will largely focus on firm side of EE

IO tools well suited to recover preferences and run counterfactuals

What does the frontier of this literature look like?

[hopefully your term paper, eventually]

  1. Test a theory
    • tough to find low hanging fruit
    • i.e. independence of allocation
  2. Measure costs and benefits
    • identification
      • SUTVA / spillovers
    • something we don’t know about (like fine PM)
    • some important extension: long vs short run; avoidance - adaptation; behavioral
    • climate change per se important (but crowded)

  1. Evaluate a policy
    • not enough unless you tie to theory/ some broader question
    • compare second (third..) best to ideal policy
    • “dumb” policies often provide nice experiments to test other hypotheses
  2. Environmental settings are good for learning about economics more broadly
    • Hunt’s papers
    • Energy markets have nice properties (undifferentiated, clear mechanisms, good data, lots of policy )

Required Readings

Cropper and Oates (1992) [link]