Now imagine that the parent, P, cares about both children. However, only the parent can make transfers. Solve for the subgame perfect equilibrium of this game. Think about how the consumption of each party varies with income on the continuation path. It is currently the only producer of these goods.
Demand is determined as follows.
There is a single consumer. The consumer buys either one unit of stuff, or none at all. Similarly, she buys either one unit of junk, or none at all. The consumer receives value R S from consuming stuff, and value R J from consuming junk. CTWE has no fixed costs.