ECON 711 Macroeconomic Theory and Policy
宏观经济理论与政策代考 Question 1. (5 points) Solow model in discrete time. Consider an economy with technological progress but without population growth that
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Question 1. (5 points) Solow model in discrete time. 宏观经济理论与政策代考
Consider an economy with technological progress but without population growth that is on its balanced growth path. Now suppose there is a one-time jump in the number of workers.
(a) At the time of the jump, does output per unit of effective labor rise, fall, or stay the same? Why?
(b) After the initial change (if any) in output per unit of effective labor when the new workers appear, is there any further change in output per unit of effective labor? If so, does it rise or fall? Why?
(c) Once the economy has again reached a balanced growth path, is output per unit of effective labor higher, lower, or the same as it was before the new workers appeared? Why?
Question 2. (5 points) Dynamic Programming. 宏观经济理论与政策代考
Consider the problem of consumption and saving out of initial wealth. The goal is to maximize
(a) Write the Bellman equation for this problem in terms of current and future states w and w’ .
(b) Using the Bellman equation, write the first order condition,.the envelope condition and derive the Euler equation for this problem. How can you interpret the Euler equation?
Question 3. (5 points) Ramsey-Cass-Koopmans model in discrete time.
(a) Rewrite the problem in per worker terms. Derive optimality conditions that characterize the solution to the planner’s problem. Give intuition for those optimality conditions.
(b) What is the steady state savings rate in this economy?
(c) Suppose the economy is initially in the steady state. Suppose that a new set of regulations makes the economy less productive decreasing TFP from A to A’ < A. Use a phase diagram to explain (i) how this change affects the long-run values of consumption, and capital and (ii) how the economy transitions to these new long-run values.
Question 4. (5 points) Solow model in continuous time. 宏观经济理论与政策代考
Consider the Solow model in continuous time with production function y = f(k) = kα , constant savings rate s, depreciation rate δ, productivity growth g and employment growth n.
(b) Derive an exact solution for the time path x(t) of capital-to-output ratio.
(c) Derive an exact solution for the time path k(t) of capital per effective worker.