Suppose that we have a standard Solow model with a Cobb-Douglas production function. The central equation of the model is as follows: kt+1 = sAkα t + (1 − δ)kt . Consumption per worker is given by: ct = (1 − s)Akα t . (a) Solve for an expression for the steady state capital stock per worker. In doing so, assume that the level of productivity is fixed at some value A. (b) Use your answer on the previous part to solve for an expression for steady state consumption per worker. (c) Use calculus to derive an expression for the s which maximizes steady state consumption per worker.
Suppose that we have a standard Solow model with a Cobb-Douglas production function. The central equation of the model is as follows: kt+1 = sAkα t + (1 − δ)kt . Consumption per worker is given by: ct = (1 − s)Akα t . (a) Solve for an expression for the steady state capital stock per worker. In doing so, assume that the level of productivity is fixed at some value A. (b) Use your answer on the previous part to solve for an expression for steady state consumption per worker. (c) Use calculus to derive an expression for the s which maximizes steady state consumption per worker.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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4. Suppose that we have a standard Solow model with a Cobb-Douglas production function. The central equation of the model is as follows:
kt+1 = sAkα
t + (1 − δ)kt
.
Consumption per worker is given by:
ct = (1 − s)Akα
t
.
(a) Solve for an expression for the steady state capital stock per worker. In
doing so, assume that the level of productivity is fixed at some value A.
(b) Use your answer on the previous part to solve for an expression for
steady state consumption per worker.
(c) Use calculus to derive an expression for the s which maximizes steady
state consumption per worker.
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