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Cobb-Douglas production function,

Cobb-Douglas production function,

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Consider the Ramsey-Cass-Koopmans neoclassical growth model with log utility, Cobb-Douglas production function, and 100% depreciation: Choose {c, ,k1,t > 0} to maximize EB' Inc, 't+1 t=0 subject to C, +k,1 = Ak“ , t20 ko given. 0<a <1,0< B<1. t+1 a) Write down the Bellman equation with (state, control) = (k, ,k,+1) . b) Solve the Bellman equation by the method of undetermined coefficients with the guess V(k) = E +F ln k. Find the optimal consumption and capital accumulation decision rules. c) Use graphical method to trace out the optimal capital sequence from the optimal capital accumulation decision rule that you find in (b). Hint: Draw the 45-degree line in (k, ,k,1) space. Suppose the economy starts with an initial capital stock that is below the steady state. How would consumption and capital evolve over time? Draw their time paths to illustrate your answer.
Transcribed Image Text:Consider the Ramsey-Cass-Koopmans neoclassical growth model with log utility, Cobb-Douglas production function, and 100% depreciation: Choose {c, ,k1,t > 0} to maximize EB' Inc, 't+1 t=0 subject to C, +k,1 = Ak“ , t20 ko given. 0<a <1,0< B<1. t+1 a) Write down the Bellman equation with (state, control) = (k, ,k,+1) . b) Solve the Bellman equation by the method of undetermined coefficients with the guess V(k) = E +F ln k. Find the optimal consumption and capital accumulation decision rules. c) Use graphical method to trace out the optimal capital sequence from the optimal capital accumulation decision rule that you find in (b). Hint: Draw the 45-degree line in (k, ,k,1) space. Suppose the economy starts with an initial capital stock that is below the steady state. How would consumption and capital evolve over time? Draw their time paths to illustrate your answer.
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