Liquidity: Its Origins and Implications in an Uncertain Multiperiod World with Limited Borrowing
Miller, Edward, American Economist
Most monetary and macroeconomic theory contains an implicit assumption that all assets and liabilities are traded in perfect markets with equal borrowing and lending rates. This paper will show that significant changes must be made in our standard theories when borrowing and lending rates differ. The frequent and important case where individuals cannot borrow against their human capital can
be handled by noting that inability (or unwillingness) to borrow is operationally equivalent to an infinite borrowing rate. The more general case of borrowing rates exceeding lending rates thus includes the inability to borrow against certain types of future income, such as income from human capital.
A monetary theory which assumes perfect financial markets with borrowers able to borrow unlimited amounts at the lending rate upon demand (and without transaction costs) is logically inconsistent. In such a world, the free and ready availability of credit makes liquidity a free good and holding noninterest paying money irrational. Since everything can be financed by credit, the optimal strategy is to invest all monetary balances and to use credit for working balances. Any monetary income is used upon its receipt to reduce the outstanding credit balances.
Most attempts to derive a theory of consumption and saving from individual behavior use two-period models in which there is an exchange of present consumption for future consumption at a specified date . Yet observation suggests that most individuals view the key decision as being a trade-off between current consumption or saving. Saving is retaining purchasing power for consumption at an indefinite and unspecified future time. The decision to save is the decision to retain the option, through asset holding, of choosing a date for future consumption.
In this essay a simple state of nature model will be used in which the consumer chooses between consumption now and retaining purchasing power for future use. The model has been developed elsewhere  and will be used here to explore the implications of different types of assets for macroeconomic equilibrium. It differs from other models with uncertain future income in being multiperiod and in having higher borrowing rates than lending rates. In such a model, the marginal utility of consumption is equated to the marginal utility of purchasing power held for future use. This leads to a model in which liquid asset holdings enter into the consumption function and are not cancelled out by liabilities of equal amount.
It will be shown here that allowing for the option on consumption aspect of holding purchasing power does not make a difference if unlimited borrowing is possible at the lending rate. However, if the consumer cannot borrow unlimited amounts at the rate at which he lends, liquidity does have value for him. An analysis of the choice between consumption now and an option on consumption gives different conclusions than the traditional analysis of the optimal choice between consumption at two times.
When the consumer can both borrow and lend at the going interest rate, the condition for consumer equilibrium between period (n - 1) consumption and period n consumption is simple. Let i be the interest rate. In equilibrium he will have borrowed (or lent) sufficient amounts in period n - 1 and in the relevant state of nature to assure that the marginal utility in period n - 1 is equal to the period n marginal utility multiplied by (1 + i). With any other relationship between the marginal utilities of consumption in the two periods, the consumer could increase his welfare by changing his level of saving. This could not be an equilibrium.
Thus, with equal lending and borrowing rates, the marginal utility of current consumption must (adjusted for interest) equal the marginal utility of next period's consumption. The consumer gains no additional utility beyond time preference from being able to spend funds early; he cannot benefit from increased liquidity and the ability to shift consumption to an earlier time. …