Mirroring: Godley, W & Lavoie, M, Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth, pp.103-105
Households make a two stage decision. In the first step, households decide how much they will save out of their income. In the second step, households decide how they will allocate their wealth, including their newly acquired wealth. The two decisions are made within the same model iteration. However, the two decisions are distinct and of a hierarchical form. The consumption decision determines the size of the end of period stock of wealth; the portfolio decision determines the allocation of the stock of wealth.
How is wealth allocated between money and bonds? Two traditions have prevailed. One related to the quantity theory of money, links money balances to the flow of income and the other, of more recent vintage, makes money balances some proportion of total wealth. The latter is related to the Keynesian notion of liquidity preference. The lower is liquidity preference, the lower is the money to wealth ratio.
The transactions demand for money and the liquidity preference story may both be comprised within a single model. Households wish to hold a certain proportion λ0 of their wealth in the form of interest-bearing bills, and hence, because there is no third asset, a proportion equal to (1 - λ0) in the form of money. This proportion, however, is modulated by two elements, the rate of return on Treasury bills and the level of disposable income relative to wealth.
Allocation function 'PropIntBills' incorporates an interpretation of G&L's Brainard-Tobin formula, slightly amended. ABMPC can run with multiple producers and households. In this system, household agents may face period(s) of unemployment with no knowledge of when they may be employed once again. If unemployed, an agent's disposable income will fall, leading (probably) to the denominator in the 'wealth to income' calculation becoming immediately smaller than the numerator; blowing up G&L's interpretation of Brainard-Tobin. Therefore, if unemployed, a household agent will adjust its allocation of interest-bearing assets to money deposits based on a 'wealth to system average income' calculation.