Suppose that an EPA must select one instrument from two available. Two criteria matter:

(a) P, the probability of the instrument attaining its target;

(b) C, the proportionate saving in abatement cost incurred in using that instrument (relative to the cost using the highest-cost instrument). The EPA calculates a weighted sum (score) for each instrument, and chooses that with the highest score. Assume that the instruments have the following values for P and C:

Instrument 1: P = 0.9, C = 0.0 Instrument 2: P = 0.7, C = 0.2

(i) Write an Excel spreadsheet to illustrate how the instrument choice varies with changes in the relative weights (between zero and one)

attached to the two criteria. Also explore how instrument choice varies as the magnitudes of P and C for each instrument vary.

(ii) Use an algebraic formulation of this problem to obtain expressions that allow these results to be shown analytically.