State-Contingent Consumption

An individual possessing an initial wealth of initial wealth is considering two potential futures concerning climate policy. In the first scenario, government policies introduce incentives for rainwater harvesting systems and energy-efficient home upgrades, leading to lower prices for these goods. In the alternate scenario, environmental regulations increase, resulting in higher prices for the same goods. These scenarios are defined as State A and State B, and they have probabilities pA and pB, respectively. The individual is interested in purchasing the two goods, rainwater harvesting systems and energy-efficient home upgrades, available in both states but at varying prices: State A features prices pA x and pA y, whereas State B exhibits prices pB x and pB y. The dollar amounts spent on the two goods must be fixed now, before it is known which state occurs; in either state those dollars buy the goods at that state's prices, and the goods are divisible. In the utility function, x is the quantity of the first good and y the quantity of the second, in the order the prices are listed, and each option gives (dollars spent on the first good, dollars spent on the second good). With a known utility function utility function, how should the individual allocate their wealth to maximize expected utility given these two potential scenarios?