4. Heterogeneity (25 points)
Consider a one-period economy with competitive markets. There are mass one households and mass
one firins. The firms use labor in units of working hours, n, to produce consumption goods, and the
production function is:
where A > 0 captures the productivity of firms. The housebold's utility is 
where the c is the consumption, n is the working hour, and the parameter,γ > O, captures the
importance of consumption to households. A household's income comes from working, and the wage
per hour is denoted by w. Thus, the household's budget constraint is
c = wn.