2. Ramsey model with AK production function. Consider an economy that is populated with a large number of identical consumers that solve the following problem: maxt=0t1Ct1>0 subject to a sequence of constraints: Kt+1=Kt(1)+It,t1 for given initial level of physical capital K0, and aggregate resource constraint: Yt=Ct+St=Ct+It. and production function Yt=AKt. (a) Write the optimization problem from social planner's perspective! Derive the first-order conditions using the Bellman equation. (b) Derive the Euler equation for optimal consumption! What is the effect of changing concavity of utility function parameter , which measures risk aversion, on consumption growth rate? (c) Determine the the long-run growth in this economy? Determine the savings rate along the balanced growth path! (Hint: Use the equality of growth rates to calculate the savings rate.) 2. Ramsey model with AK production function. Consider an economy that is populated with a large number of identical consumers that solve the following problem: maxt=0t1Ct1>0 subject to a sequence of constraints: Kt+1=Kt(1)+It,t1 for given initial level of physical capital K0, and aggregate resource constraint: Yt=Ct+St=Ct+It. and production function Yt=AKt. (a) Write the optimization problem from social planner's perspective! Derive the first-order conditions using the Bellman equation. (b) Derive the Euler equation for optimal consumption! What is the effect of changing concavity of utility function parameter , which measures risk aversion, on consumption growth rate? (c) Determine the the long-run growth in this economy? Determine the savings rate along the balanced growth path! (Hint: Use the equality of growth rates to calculate the savings rate.)