Consider an economy populated by a large number of identical

households of mass one whose preferences are given by

Question 1 Consider an economy populated by a large number of identical households of mass one whose preferences are given by U = / u(c(t) )e-pt L(t) at u(c) = 1-0 where c is consumption per capita, p > 0, 0 > 0. Every household consists of L(t) members and each member inelastically provides one unit of labor. There- fore L(t) represents the aggregate labor force of the economy. Output is produced according to a Cobb Douglas production technology: Y ( t ) = K (t ) " ( A ( t ) L ( t ) ) 1- a with 0