2. RBC model with exogenous labour supply - a la RCK model. Consider an economy that is populated with a unitary mass of agents. The social planner pursues the following utility function: maxt=0t1Ct1,>0 where denotes a period discount factor and Ct is the total consumption. The planner accumulates physical capital according to the following law of motion: Kt+1=Kt(1)+It, and aggregate resource constraint: Yt=Ct+St=Ct+It. The planner organizes production and transforms inputs into outputs with Cobb-Douglas production function: Yt=AtKtLt1 Technological index evolves as: logAt+1=logAt+t,00,>0 where Lt is labor. For this utility we derived the following log-linearized law of motion for capital: K^t+1=(1++1)K^t+KY+1+A^t(KC++1KY)C^t Compare this expression to the one you derived in (d) and comment the differences between the two. Focus on parameter that reflects the preference for leisure, , which was assumed to be 0 throughout this exercise (from (a) to (d)), while it was positive in the standard RBC model with endogenous labor supply. Is parameter affecting intertemporal substitution of labor? 2. RBC model with exogenous labour supply - a la RCK model. Consider an economy that is populated with a unitary mass of agents. The social planner pursues the following utility function: maxt=0t1Ct1,>0 where denotes a period discount factor and Ct is the total consumption. The planner accumulates physical capital according to the following law of motion: Kt+1=Kt(1)+It, and aggregate resource constraint: Yt=Ct+St=Ct+It. The planner organizes production and transforms inputs into outputs with Cobb-Douglas production function: Yt=AtKtLt1 Technological index evolves as: logAt+1=logAt+t,00,>0 where Lt is labor. For this utility we derived the following log-linearized law of motion for capital: K^t+1=(1++1)K^t+KY+1+A^t(KC++1KY)C^t Compare this expression to the one you derived in (d) and comment the differences between the two. Focus on parameter that reflects the preference for leisure, , which was assumed to be 0 throughout this exercise (from (a) to (d)), while it was positive in the standard RBC model with endogenous labor supply. Is parameter affecting intertemporal substitution of labor