2. (34 points) Keeping Up with the Joneses - Consider a static (one-period) economy inhabited by two households indexed by i = 1, 2. Household i can either work (n;) or enjoy leisure (1,). Each household i is endowed with one unit of time, Itn, = 1. When working, households earn the wage w which they can use to purchase consumption goods. Households derive utility from their own consumption & only relative to the other type's consumption, i.e., they get more utility if they know they consume more than their neighbor. Preferences for agent i are therefore U (c, Cixj, 4) = In +ylnl (1) with # e (0, 1), and similarly for household 2. Firms hire labor in a competitive labor market, and produce with the linear tech