2. There is a representative innitelylived consumer with preferences given by 2 5f\" {91: it} i=0 1 where c: is consumption and l; is leisure. u (-j is strictly concave and .3 = T where p :> D is time preference rate. Each period consumer has one unit of time which can be supplied as labor and earns wage rate wt per hour. The consumer owns the capital kg at the beginning of period 0 which he can rent at rental rate rt. Capital depreciates at rate 6 each period. The representative rms has a constantreturnstoscale production technology Y; = 2F {Nb IQ), and maximizes prots at each period hiring labor N; and capital K; at rate is; and rt, respectively. (a) Dene a competitive equilibrium of this economy (b) 1Write down a social planner's problem of this economy. (c) Show that the social planners allocation is equivalent to the competitive equilibrium