Compute steady state value of capital - solow growth model, Mathematics

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Consider the Solow growth model as given in the lecture notes using the Cobb-Douglas production function

Y_t = AK^1-α_t L^α_t

a) Set up the underlying nonlinear difference equation.

b) Compute the steady state value of capital.

c) Linearize the nonlinear difference equation around the positive steady state and determine its properties.

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