Households, Government and Investment

Households, Government and Investment#

The standard model contains three final-demand blocks.

Household demand#

Households allocate disposable factor income across goods using calibrated Cobb-Douglas expenditure shares:

\[X_i^p = \frac{\alpha_i}{p_i^q} \left( \sum_h p_h^f FF_h - S^p - T^d \right).\]

Government demand#

Government consumption depends on tax revenue net of government saving:

\[X_i^g = \frac{\mu_i}{p_i^q} \left( T^d + \sum_j T_j^z + \sum_j T_j^m - S^g \right).\]

Investment demand#

Investment demand is allocated using fixed shares:

\[X_i^v = \frac{\lambda_i}{p_i^q} \left( S^p + S^g + \varepsilon S^f \right).\]

Private and government saving are themselves defined as calibrated fractions of their respective income bases:

\[S^p = ss^p \sum_h p_h^f FF_h,\]
\[S^g = ss^g \left( T^d + \sum_j T_j^z + \sum_j T_j^m \right).\]

These equations mean that a policy shock can affect final demand indirectly through income, taxes, saving and prices even when the shock is applied somewhere else in the model.

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