Exposition of the Individual Benefit-Cost Approach

A Mathmatical Exposition of the Individual Benefit-Cost Approach 

As stated in Chapter 2 the focus of the individual benefit-cost approach is on the roadway user s choice of a target level of safety and choice of ways of achieving that safety. For expositional purposes the approach is couched in terms of motorist behavior and striking examples. The approach applies, however, to all roadway users and includes subtle responses which may occur over extended periods of time. The approach is general in that mandated technological changes and responses based on psychophysiological arousal are incorporated.  

A motorist will experience one of two states of the world either an accident does not occur or an accident occurs over some period of time. The probability that a motorist is involved in an accident (p) is influenced by the driver s own safety effort (e) and government safety measures (s). The production function for accident risk is specified by p(e,s) with pe 0, pee 0, ps 0, pss 0, and pes 0 where the signs of the first and second derivatives shown represent typical production conditions. For example ps 0 means that the partial effect of an increase in enforcement activity against drunk driving would reduce the probability of an accident. The loss which a motorist incurs in an accident (L) depends on the motorist s own safety effort and government safety measures also L(e,s) with Lc 0, Lee 0, Ls 0, Lss 0, and Les 0. The expected loss from an accident is determined by the probability of an accident as well as the size of the loss. Notice that the assumption pes 0 and Les 0 reflect the individual and government safety efforts are similar and are substitutes in production. I%ally, let there be disutility (V) associated with driver safety effort V(e) with Ve 0 and Vee 0. 

if the motorist has income (I) and is risk neutral, then expected utility is shown in Equation 1  

Equation 1 shows that expected utility equals the probability of an accident times the payoff if an accident occurs, plus the probability of no accident times the payoff if no accident occurs. More simply expected utility is income less disutility less the expected accident loss. In balancing the benefits and costs of safety effort the motorist increases effort through use of safety belts and moderate speeds or similar activity until dU/de = 0 or as shown in Equation 2  

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