Consider an economy with identical households who are distributed on the unit interval. Social planner faces the following problem: x Bu(c) max subject to (1) c +kt+1 = [(1 Xt)kt] + (1 8) kt (2) Ct, kt+1 0 and ko > 0 given where a (0, 1) and Xt [0, 1] is the fraction of capital allocated to improve environmental quality. Assume a typical utility function: strictly concave, strictly increasing, and (at least) twice differen- tiable. Suppose that the planner solves the above problem taking Xt as given; it is controlled by the Environmental Protection Agency (EPA). 3. Suppose that the EPA decides to increase Xt from X to x' where x'>x because their concern for the environment has increased. Assume that the EPA announces at t = 0 that xt = x' is implemented from t = 0 and the change is permanent (hence unanticipated permanent policy change). Assume that it is t = 0 now and the economy is at the steady state. As was learned at the class, assume that income effect dominates substitution effect. What happens to this economy? Go as far as you can in describing the behavior of capital and consumption from t > 0 using diagrams. (20 points) Consider an economy with identical households who are distributed on the unit interval. Social planner faces the following problem: x Bu(c) max subject to (1) c +kt+1 = [(1 Xt)kt] + (1 8) kt (2) Ct, kt+1 0 and ko > 0 given where a (0, 1) and Xt [0, 1] is the fraction of capital allocated to improve environmental quality. Assume a typical utility function: strictly concave, strictly increasing, and (at least) twice differen- tiable. Suppose that the planner solves the above problem taking Xt as given; it is controlled by the Environmental Protection Agency (EPA). 3. Suppose that the EPA decides to increase Xt from X to x' where x'>x because their concern for the environment has increased. Assume that the EPA announces at t = 0 that xt = x' is implemented from t = 0 and the change is permanent (hence unanticipated permanent policy change). Assume that it is t = 0 now and the economy is at the steady state. As was learned at the class, assume that income effect dominates substitution effect. What happens to this economy? Go as far as you can in describing the behavior of capital and consumption from t > 0 using diagrams. (20 points)