a. Find the F.O.C. for this problem. Note: F.O.C. also includes the costate equation along with the other relevant equations.

b. What is the effect on steady state supply of labor if there is a rise in ?? Show all calculations.

4. An innitely lived representative agent has the following utility over consumption and leisure, U [(7, I] = log(c) + ylog (l), where c is the consumption per capita and y > 0. The consumer has a time endowment of 1 unit, whichis split between labor and leisure, i.e. 1 2 Mt) + Kt), denotes the time constraint of the consumer. Production of the nal good in this economy is done by using capital and labor, using the following production function, Y = F [K . L] = AK'ILI'\". Population growth is zero. The technology growth is zero. Assume that population size is normalized to 1, so per capita and level variables mean the same thing. Thus, capital per capita is given by k = K. Furthermore, capital stock depreciates at the constant rate 6 > 0. A planner optimizes the utility function U[c, I] discounted by the rate of time preference p subject to the time constraint and the budget constraint of the consumer. The resource constraint for the planner is given by, K=F[K,L]C6K a. Find the F.O.C. for this problem. Note: F.O.C. also includes the costate equation along with the other relevant equations. b. What is the effect on steady state supply of labor if there is a rise in 6? Show all calculations