Suppose that an EPA must select one instrument from two available. Two criteria matter: (a) P, the..

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
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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.

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