Isabel's preferences for leisure L and consumption C can be expressed as U(C, L) = (C - 200) x (L - 80), implying that her marginal utility of leisure is (C - 200) and her marginal utility of consumption is (L - 80). The most leisure she can consume in any given week is 168 hours. Isabel earns $8 per hour after taxes.
1. Identify her optimal amount of leisure and consumption, and her total utility.
2. Now Isabel can sign up for government welfare benefits. The benefit is determined by the formula B = $220 - (Earnings) x (.5). Identify her optimal amount of leisure and consumption. Will she sign up for welfare benefits?