Advanced Topics
Money Supply Growth
In BOMD, money supply grows through:
\[\frac{dM}{dt} = \underbrace{Credit}_{\text{Private}} + \underbrace{(Spend_{Gov} + Int_{Gov} - Tax)}_{\text{Government}}\]
Both private lending and government deficits create money.
Price Level Dynamics
Adding inflation requires price equation:
\[\frac{dP}{dt} = P \times \left(\frac{Demand - Supply}{Supply}\right) \times \text{adjustment speed}\]
Where: - Demand includes consumption, investment, government spending - Supply is productive capacity - Inflation occurs when demand exceeds supply
International Trade
Adding foreign sector:
\[\frac{dPrivate_{Equity}}{dt} = \underbrace{(Spend_{Gov} + Int_{Gov} - Tax)}_{\text{Fiscal}} + \underbrace{(Exports - Imports)}_{\text{Trade}}\]
The sectoral balances identity becomes:
\[\text{Government Balance} + \text{Private Balance} + \text{Foreign Balance} = 0\]
Capital Adequacy
Banks require minimum equity ratios:
\[\text{Capital Adequacy Ratio} = \frac{Banks_{Equity}}{Debt_{Firms} + Debt_{Gov}} \geq \text{minimum (e.g., 8\%)}\]
Model bank failures when equity becomes negative.
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