Endogenous variables’ equations

Investement \[I = Y - CH - G \tag{1}\]

Production (GDP) \[Y . p = w . L + p . \left( \delta + r \right) . K \tag{2}\]

Households’consumption \[CH = \left( 1 - \sigma \right) . \frac{\left( w . L + p . r . K \right)}{p} \tag{3}\]

Wage (from cost minimization assuming a CES function) \[w + L = \left( \left( \frac{Y}{PROG^{L}} \right) . \left( \left( \varphi^{L} \right) ^ {\rho} \right) . \left( \frac{w}{\left( p . PROG^{L} \right)} \right) ^ {\left( -\rho \right)} \right) + w \tag{4}\]

Interest rate (from cost minimization assuming a CES function) \[r + K = \left( \left( \frac{Y}{PROG^{K}} \right) . \left( \left( \varphi^{K} \right) ^ {\rho} \right) . \left( \frac{\left( \delta + r \right)}{PROG^{K}} \right) ^ {\left( -\rho \right)} \right) + r \tag{5}\]

Capital (from accumulation equation) \[\varDelta \left(K\right) = I_{t-1} - \delta . K_{t-1} \tag{6}\]

Price \[p = 1 \tag{7}\]