Consider a variant on the defensive expenditure model presented in this chapter. Suppose air pollution is the nonmarket bad and soap is the market good that can reduce the effects of air pollution-we bathe more frequently and wash our possessions more frequently. Our personal hygiene \((H)\) is determined by the pollution level \((P)\) and soap used (S). Suppose the price of soap is \(p_{s}\). Set up the consumer's utility maximization problem for choosing the right amount of soap, other goods \((x)\), and perhaps \(H\) and \(P\). You do not need to solve the problem.