Consider a Solow model in discrete time with A(t) = L(t) = 1 and the following production functionF(K) = {√R-Kif K € (0, K)if K € [K, +∞o)*Other parts of the model including the capital depreciation rate & and saving rates are still constant parameters.(a) Prove that for V(6, s) € (0, 1)², there exists K> 0 s.t. the model has two steady-state equilibria.(b) When there are two steady-state equilibria, find the range of K(0) s.t. K(t) converges monotonically to atleast one of the steady-states.(c) Given parameters {8, K}, find the range of parameter s, s.t. the economy always fails to grow.

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K-K if K € [K, +∞)* pital depreciation rate 8 and saving rate s are still consta exists K> 0 s.t. the model has two steady-state equilil ilibria, find the range of K(0) s.t. K(t) converges mon nge of parameters, s.t. the economy always fails to gr

K-K if K € [K, +∞)* pital depreciation rate 8 and saving rate s are still consta exists K> 0 s.t. the model has two steady-state equilil ilibria, find the range of K(0) s.t. K(t) converges mon nge of parameters, s.t. the economy always fails to gr

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

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Consider a Solow model in discrete time with A(t) = L(t) = 1 and the following production function
F(K) = {√R-K
if K € (0, K)
if K € [K, +∞o)*
Other parts of the model including the capital depreciation rate & and saving rates are still constant parameters.
(a) Prove that for V(6, s) € (0, 1)², there exists K> 0 s.t. the model has two steady-state equilibria.
(b) When there are two steady-state equilibria, find the range of K(0) s.t. K(t) converges monotonically to at
least one of the steady-states.
(c) Given parameters {8, K}, find the range of parameter s, s.t. the economy always fails to grow.

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