Time Allocation with Log-Log Preferences
Robinson has preferences described by the utility function u(c, 1) = log c+lnl, where c denotes consumption and I leisure. Assume that the total number of available hours is equal to one so that 1+ h = 1. The production function is y = Ah, with 0 < a < 1.
(a) What is the optimal choice of hours worked, h*?
(b) What happens to h* if A rises?
(c) What happens to h* if we increase the value of ?