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Production functions with this property include
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* the ** Cobb-Douglas** function $F(K, L) = A K^{\alpha}
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- L^{1-\alpha}$ with $0 \leq \alpha \leq 1$ and
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+ L^{1-\alpha}$ with $0 \leq \alpha \leq 1$.
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* the ** CES** function $F(K, L) = \left\{ a K^\rho + b L^\rho \right\} ^{1/\rho}$
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- with $a, b, \rho > 0$.
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+ with $a, b, \rho > 0$.
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+
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+ Here, $\alpha$ is the output elasticity of capital and $\rho$ is a parameter that determines the elasticity of substitution between capital and labor.
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We assume a closed economy, so aggregate domestic investment equals aggregate domestic
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saving.
@@ -81,6 +83,7 @@ Setting $k_t := K_t / L$ and using homogeneity of degree one now yields
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$$
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k_{t+1}
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+ = s \frac{F(K_t, L)}{L} + (1 - \delta) \frac{K_t}{L}
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= s \frac{F(K_t, L)}{L} + (1 - \delta) k_t
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= s F(k_t, 1) + (1 - \delta) k_t
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$$
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