The idea behind defensive expenditures is that it is often possible to observe changes in defensive expenditures that correspond to changes in levels of pollution (or another nuisance). The change in expenditures can be used to infer something about utility, and thus willingness to pay to avoid the nuisance. Here is an algebra example. A representative consumer has a utility function over water quality Q and all other goods X. They have exogenous total income equal to $200. The price of X is normalized to 1. Their utility is U = 100Q 10Q2 + X. To create water quality, the consumer must spend money on filtration and water supplies. The cost of achieving a given water quality level depends on the amount of ambient water pollution, denoted P. Specifically, the total expenditure required to achieve Q is given by the function D PQ. If you ponder the equations, you should see that they imply a linear, downward sloping marginal benefit curve for Q, and a linear upward sloping marginal cost curve for Q, which changes slope when P changes. 6. Suppose that the initial ambient water pollution is equal to P = 2.5. What quantity of Q will the consumer choose? If necessary, round your answer to three decimal places. (1 point) Answer: 7. Now suppose that the initial ambient water pollution rises so that P = 6. What quantity of Q will the consumer choose now? If necessary, round your answer to three decimal places. (1 point)