ABMPC Accounting

Opening

Description
Balance Sheet (Stocks):Stocks of assets have a plus sign.
 Stocks of liabilities have a minus sign.
 
Transactions Matrix (Flows):All sources of funds appear with a plus sign - these are the incoming flows of money.
 All uses of funds appear with a minus sign.
Balance Sheet
 HouseholdProductionGovernmentCentral BankSum
Money+H  -H0
Bills+Bh -B+Bcb0
Balance (Net Worth)-V +V 0
Sum0 000

Matrix

Transactions / Behavioural flow matrix of ABMPC
G20.00Θ0.2r0.1α10.6λ0.5   
 Model Iteration 0HouseholdProductionGovernmentCentral BankSum
     CurrentCapital 
 Consumption-9.60-Cd9.60+Cs      0
 Govt. Expenditures  20.00+Gs-20.00-Gd    0
 [OUTPUT]   [Y]      0
 Factor Income (Wage)20.00+W・Ns-20.00-W・Nd      0
 Interest Payment (Household)0.00+r (t-1)・Bhd (t-1)  0.00-r (t-1)・Bhs (t-1)    0
 Interest Payment (Central Bank)    0.00-r (t-1)・Bcbs (t-1)0.00+r (t-1)・Bcbd (t-1)  0
 Central Bank Profit    0.00+r (t-1)・Bcbs (t-1)0.00-r (t-1)・Bcbd (t-1)  0
 Taxes-4.00-Ts  4.00+Td    0
 Equity (Wealth)6.40          
 Change in CB deposits-3.20-ΔH      3.20+ΔH0
 Change in Bills-3.20-ΔBh  16.00+ΔB  -12.80-ΔBcb0
Following Iteration
-0.32Interest Payment to Household
-1.28Interest Payment to Central Bank
1.28Profit Distributed by Central Bank

Balance

Transactions Accounting of ABMPC
G20.00Θ0.2r0.1α10.6λ0.5   
 Model Iteration 0HouseholdProductionGovernmentCentral BankSum
  AssetLiabilityAssetLiabilityAssetLiabilityCurrentCapital 
  AssetLiabilityAssetLiability 
 Consumption 9.609.60       0
 Govt. Expenditures  20.00  20.00    0
 Factor Income (Wage)20.00  20.00      0
 Interest Payment (Household)0.00    0.00    0
 Interest Payment (Central Bank)     0.000.00   0
 Central Bank Profit    0.00  0.00  0
 Taxes 4.00  4.00     0
 Change in CB deposits3.20        3.200
 Change in Bills3.20    16.00  12.80 0
 Equity6.409.6016.000.000.000

Code

Code Sequence

class Government(Agent):
    self.breed = "Government"
    
    def step(self) -> None:
        '''
        ABMPC Government Functions (each and every iteration):
        1 Distrubute pure expenditure to producers.
        2 Pay interest, if any, on bills held in the economy. (t-1)
        3 Calculate the amount of Treasury bills for offer. (t)
        '''

class Producer(Agent):
    self.breed = "Producer"

    def step(self) -> None:
        '''
        ABMPC Producer Functions (each and every iteration):
        1 Account for government demands.
        2 Account for household demands.
        3 Communicate to employed household agents their wage this iteration.
        '''

class Household(Agent):
    self.breed = "Household"

    def step(self) -> None:
        '''
        ABMPC Household Functions (each and every iteration):
        1 Calculate disposable income, the wage & interest received minus tax.
        2 Consumption Decision: Decide how much to save out of income.
        3 Portfolio Decision: Calculate wealth and allocate between money and bills.
            Two Traditions:
            Quantity theory of money: Link money balances to the flow of income.
            Liquidity preference: Make money balances some proportion of wealth.
        '''

        # 2
        '''
        G&L Equations, p104:

        α1 : Propensity to consume out of regular income.
        α2 : Propensity to consume out of past wealth.
        λ : Reaction parameters in the portfolio choice of households.
        λ0 : Proportion of wealth held in bills.
        (1 - λ0) : Proportion of wealth held in central bank deposits (high-powered money).


        (4.4) V = V_-1 + (YD - C): New wealth is past wealth plus disposable income minus consumption.
        (4.5) C = α1 * YD + α2 * V_-1: Propensity to consume out of disposable income + propensity to consume out of past wealth.
        (4.6) Hh = V - Bh
        (4.7) Bh/V = λ0 + λ1 * r - λ2 * (YD/V)        
        '''

        # 3
        '''
        Proportion of money balances modulated by two elements:
            1: The rate of return r on bills.
            2: The level of disposable income (YD) relative to wealth.

            G&L p104: The share of wealth which agents wish to hold in the form of money deposits
            is negatively related to the interest rate and positively related to disposable income.

            Reverse: The share of wealth which agents wish to hold in the form of bills
            is positively related to the interest rate and negatively related to disposable income.

            (Translation: 1. The share of wealth an agent will wish to hold as bills will increase with a higher 
            interest rate. Therefore, a lower proportion of wealth will be held as deposits. If the interest rate decreases,
            an agent will lower the proportion of their wealth held as bills, which will increase, as a residual, the
            proportion held as deposits.)

            (Translation: 2. The lower the level of disposable income to wealth, the higher the proportion
            of their wealth an agent will wish to hold as bills. The higher the level of disposable income to 
            wealth, the lower the proportion of their wealth an agent will wish to hold as bills, and as a
            residual, the higher will be the proportion held as deposits.)
        '''

class CentralBank(Agent):
    self.breed = "CentralBank"
    
    def step(self) -> None:
        '''
        ABMPC CentralBank Functions (each and every iteration):
        1 Set the rate of interest on bills.
        2 Distribute profit on Government bills back to the Government. (t-1)
        3 Purchase government bills surplus to household requirements. (t)
        '''

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