Consider individuals of types 1, 2, and 3. These individuals have preferences over hours of leisure per year (L) and dollars of consumption per year (c). Their preferences are the following:

u1(L,c) = L * c

u2(Lc) = L2 * c

u3(L,c) = L3 * c

The economy these three types of individuals live in has a perfectly-competitive labor market that pays a constant wage of $10 per hour (i.e. w = $10). Furthermore, assume all individuals only have 2,000 hours of time in the year (H = 2,000) to split between labor (H) and leisure.

1. What are the utility-maximizing bundles of leisure and consumption for each type of individual given in this economy?
2. What is the utility for each type of individual for their respective utility-maximizing bundles?
3. Given the transfer program described in part v, individuals have no incentive to work less than how many hours? Show your work.
4. Which type(s) of individuals will engage in "moral hazard" and cut work completely once the transfer program is in place? How do you know?