Equations of the Minsky model

The equations articulate the following model:

The Bank has two accounts: the Vault (BankVault) that acts as the source of cash - initially 100; and the Bank's asset account (BankAssets) that processes interest payments and Bank consumption.

The Firm has two accounts: a loan account (LoanTotal) that stores the amount loaned from the Bank; and a Deposit account (FirmDeposit) that processes interest payments and wages paid to employees.

These accounts are kept separate so that the model can use the LoanTotal to determine the loan repayment.

The workers have a single Deposit account (WorkerDeposit) that processes wages and consumption.

The Bank lends money from the Vault at the rate Lend and this is repaid at the rate RepayLoan.

The loan account of the Firm changes at a rate that is the negative of the Bank Vault rate of change.

The Bank assets account (separate from the Bank Vault) increases as the Firm pays interest on the loan (LoanInterest) and decreases as the Bank consumes (ConsumeB).

The workers' Deposit account increases with Wages and decreases with consumption (ConsumeW).

The rates are all per unit time (one year).

The Firm pays wages at a rate proportional to its total assets. The rate is set at WageRate = 2

The Firm repays the loan at a RepayRate[loan] = 1/7 = 0.143

The Bank consumes the output of the Firm at ConsumeRate[Bank] = 1

The Workers consume the output of the Firm at ConsumeRate[Wages] = 26

The Bank lends at a rate proportional to the amount currently in the Vault. The rate is set at LendRate = 0.75

Starting with the initial conditions specified, the model reaches stasis after about 6 years.

The rate of change of the term FirmDeposit starts off negative due to the initial consumption and deposit balances being zero. The simple monotonic trajectories ensure that the FirmDeposit remains negative for all time. This circumstance could be made less unrealistic by starting with a suitable balance in the Firm's deposit account.