When it comes to vehicle performance, there is often a tradeoff between speed & acceleration and safety features (high performance sports cars often have fewer safety features than do, say, minivans). Superior speed and acceleration are generally desirable but greater speeds increase the probability of car accidents, some fatal, some not fatal.
Consider a consumer who is choosing between safety features and speed when buying a car. From his car-buying budget, he is willing to pay Ps for a one percent reduction in the probability of a fatal accident. He is willing to Pa for a one percent increase in speed & acceleration. As far as indifference curves go, he does consider speed and safety to be imperfect substitutes with diminishing marginal rates of substitution between the two attributes.
Suppose the government mandates safety features (the cost of which are borne only by car manufacturers) on all cars that will reduce fatal accident probabilities by 25 percent. Will the safety feature mandates guarantee and reduction in overall car accidents? Explain your answer graphically using consumer theory.