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lines changed Original file line number Diff line number Diff line change 5555Production functions with this property include
5656
5757* the ** Cobb-Douglas** function $F(K, L) = A K^{\alpha}
58- L^{1-\alpha}$ with $0 \leq \alpha \leq 1$ and
58+ L^{1-\alpha}$ with $0 \leq \alpha \leq 1$.
5959* the ** CES** function $F(K, L) = \left\{ a K^\rho + b L^\rho \right\} ^{1/\rho}$
60- with $a, b, \rho > 0$.
60+ with $a, b, \rho > 0$.
61+
62+ Here, $\alpha$ is the output elasticity of capital and $\rho$ is a parameter that determines the elasticity of substitution between capital and labor.
6163
6264We assume a closed economy, so aggregate domestic investment equals aggregate domestic
6365saving.
@@ -81,6 +83,7 @@ Setting $k_t := K_t / L$ and using homogeneity of degree one now yields
8183
8284$$
8385 k_{t+1}
86+ = s \frac{F(K_t, L)}{L} + (1 - \delta) \frac{K_t}{L}
8487 = s \frac{F(K_t, L)}{L} + (1 - \delta) k_t
8588 = s F(k_t, 1) + (1 - \delta) k_t
8689$$
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