Our derivation of the Weitzman theorem has proceeded by assuming that the uncertainty in the abatement cost and damage functions (ε and η, respectively) are uncorrelated. If we generalize the problem and allow COV(ε,η)≠0, a slightly different expression for Δ as shown in Eq. (4.17) arises. Consider the case of correlated uncertainty to:

Equation 4.17

(a) derive an explicit expression for Δ in the general case. See Weitzman (1974), p.485, footnote 1 for guidance on how our derivation in the appendix must be modified;

(b) describe how positive or negative correlation in damages and abatement costs augments the purely slope-based arguments from the independence case.
Stavins (1996) argues that the type of correlation we might expect to see in many situations will lead us to favor quantity instruments, all else being equal. Summarize his arguments, and comment on the extent to which you agree.

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- ESC (7) ESCO (E) = 0 (4 K) 2 (K) (4.17)