Endogenous variables’ equations

Production (GDP) \[Y = CH + I + G \tag{1}\]

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

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

Labor demand \[L = \left( \frac{Y}{PROG^{L}} \right) . \left( \left( \varphi^{L} \right) ^ {\rho} \right) . \left( \frac{w}{\left( p . PROG^{L} \right)} \right) ^ {\left( -\rho \right)} \tag{4}\]

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

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

Investment \[\varDelta \left(\operatorname{log} I\right) = \varDelta \left(\operatorname{log} K^{n}_{t-1}\right) + alpha^{I,Kn} . \operatorname{log} \frac{K^{n}_{t-1}}{K_{t-1}} \tag{7}\]