宏观经济理论与政策代写 ECON 711代写 宏观经济作业代写

ECON 711 Macroeconomic Theory and Policy

Assignment 2

宏观经济理论与政策代写 Question 1. (2 points) Solow model in continuous time.Consider the Solow model in continuous time with production function y = f(k) satisfying

Question 1. (2 points) Solow model in continuous time. 宏观经济理论与政策代写

Consider the Solow model in continuous time with production function y = f(k) satisfying the usual properties, constant savings rate s, depreciation rate δ, productivity growth g and employment growth n.

(a) Use the implicit function theorem to show how an increase in s affects the steady state values k^∗ , y^∗ , c^∗ . Does this change in s increase or decrease long run output and consumption per worker? Explain.

(c) Derive an exact solution for the time path k(t) of capital per effective worker.

(d) Calculate and plot the time paths of k(t), y(t), c(t) starting from the initial condition k(0) = k^*/2. How long is the half-life of convergence?

(e) Now suppose that we are in steady state k(0) = k^* when the savings rate suddenly increases to s = 0.22. Calculate and plot the time paths of k(t), y(t), c(t) in response to this change.

Explain both the short-run and long-run dynamics of k(t), y(t), c(t). What if instead the savings rate had increased to

s = 0.30? Do you think these are large or small effects on output? Explain.

Question 2. (3 points) Natural resource depletion in the Solow model. 宏观经济理论与政策代写

(a) Let g_Y(t) and g_K(t) denote the growth rates of output and the capital stock. Derive a formula for g_Y(t) in terms of g_K(t).

(c) Does the economy necessarily converge to a balanced growth path? Explain.

This subsection is not graded

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