宏观经济作业代写 ECON 711代写

ECON 711 Macroeconomic Theory and Policy

宏观经济作业代写 Derive optimality conditions that characterize the solution to the planner’s problem.Give intuition for those optimality conditions.

Problem Set 2 宏观经济作业代写

Module 2-1: The Neoclassical Growth Model in Discrete Time

1.Ramsey-Cass-Koopmans model. model. Suppose the planner seeks to maximize the intertemporal utility function

subject to the sequence of resource constraints

C_t + K_t₊₁ = F(K_t , AL) + (1 − δ)K_t , 0 < δ < 1

given initial K0 > 0. Suppose for simplicity that the labor force L and the level of productivity A are constant. Let ct , kt , yt etc. denote consumption, capital, output etc in per worker units. Suppose that the period utility function and the production function have their usual properties.

(a) Derive optimality conditions that characterize the solution to the planner’s problem.Give intuition for those optimality conditions. Explain how these optimality conditions pin down the dynamics of c_t and k_t. 宏观经济作业代写

(b) Now suppose that the production function is Cobb-Douglas, Y = F(K, AL) = Kα(AL) 1−α with 0 < α < 1. Derive expressions for the steady state values k ∗ , y∗ , c∗ in this economy. How do these steady state values depend on the period utility function? Explain.

(c) What is the steady state savings rate in this economy? Explain how the steady state savings rate depends on the parameters α, β, δ and the level of productivity A. Give intuition for your answers.

(d) Suppose the economy is initially in the steady state you found in (b). Suppose the economy becomes more patient with the discount factor increasing from β to β 0 > β. Use a phase diagram to explain (i) how this change affffects the long-run values of consumption,capital and output, and (ii) how the economy transitions to these new long-run values. How would your answers diffffer if the discount factor fell from β to β 0 < β. ?