Say the household has utility
u(c,l) = c + log(l), and is endowed with h=1 units of time and no units of capital. The government has planned expenditures of G=1. The firm's production technology is Y = N^1/ 2.
(a) State and solve the household's problem.
(b) State and solve the firm's problem.
(c) Do wages clear when the wage equals two? Do we know whether the equilibrium wage is higher or lower than two?
(d) Now say a wave of technological advances increases productive capacity toY = 4N^1/ 2. Domarkets clear now when the wage equals two? Do we know whether the equilibrium wage is higher or lower than two?
(e) From our answers in (c) and (d), can we conclude anything about the effects of the increase in productivity on equilibrium wages?