Government Money with Model Portfolio Choice (PC)

Model PC involves a combination of the circular flow of income approach with the stock approach. This allows us to view money as both "a device allowing transactions between agents to take place" & "a financial asset which agents hold for investment purposes".
A central bank that can offer bills (B) at the rate of interest, r, is also added to Model PC. Using r on an asset, the agent can decide whether it is preferable to hold money or another financial asset.

Note: r is held constant over the entire period of the bond to avoid the inclusion of capital gains on the asset, thus simplifying the model.

Balance Sheet for Model PC

The household has private wealth, V, which is the sum of money, H, and bonds, Bh.
Private wealth is equal to public debt which is held by the Government, +V. This, in turn, is equal to the sum of bonds held by the household and the central bank. This allows all rows & columns to sum to zero.

Transaction Flow For The Economy

To take all transactions into account, the rows & columns each sum to zero.
With this new flow, we must incorporate the bonds issued by the Central Bank (CB) & the payments generated for households as a result of interest payments.

The inclusion of the CB sees a marked change from Model SIM with its capital & accounts components. "Current account describes inflows & outflows that form the current operation on existing assets or liabilities & salaries of CB. Capital account describes changes in the balance sheet of the CB for instance, when it purchases new bills." Additionally, any profits the CB makes are redistributed to the government giving the CB a net worth of zero.

The Equations Of Model PC

(1) National Income: Remains unchanged
(2) Disposable Income: Interest payments on government debts are added to this equation.
(3) Taxable Income: Similar to (2)
(4) Reflects the change in total wealth as a result of the difference between disposable income & consumption.
(5) Consumption function now has total wealth instead of money (SIM) as second argument. It's important the conditions are met or the economy would run out of money.

The Portfolio Decision
The PC model requires that the households decision making process is divided into two stages:
1 - A decision on the proportion to allocate to consumption & saving.
2 - A decision on the allocation of the households acquired wealth during current & previous periods.

The household wants to hold a proportion of their wealth in bonds and the remaining proportion in money. the allocation is decided by the attractiveness of the interest rate. The higher the return on bonds, the higher the proportion of wealth will be allocated.
(6) Describes the amount of money to be held taking into account the interest rate & level of disposable income to wealth.
(7) Describes the amount of bonds to be held using the same weightings as (6) but in reverse.
(8) Balancing condition: 1 = (Hh/V) - (Bh/V)


(9) Government deficit is financed by bills newly issued by the Treasury department.
(10) changes in supply of money equal changes in supply of bonds
(11)Explains how the demand to hold bonds as assets over money is determined with the use of the interest rate(12).

Quotes referenced from Godley & Lavoie, chapter 3, pages 99-107