economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...

and

finance Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Admin ...

, an intertemporal budget constraint is a constraint faced by a

decision maker In psychology, decision-making (also spelled decision making and decisionmaking) is regarded as the cognitive process resulting in the selection of a belief or a course of action among several possible alternative options. It could be either ra ...

who is making choices for both the present and the future. The term intertemporal is used to describe any relationship between past, present and future events or conditions. In its general form, the intertemporal budget constraint says that the

present value In economics and finance, present value (PV), also known as present discounted value (PDV), is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money ha ...

of current and future cash outflows cannot exceed the present value of currently available funds and future cash inflows. Typically this is expressed as :

\sum_^T \frac  \le \sum_^T \frac ,

where

x_t

is expenditure at time ''t'',

w_t

is the cash that becomes available at time ''t'', ''T'' is the most distant relevant time period, 0 is the current time period, and

\frac{1+r}

is the

discount factor In finance, discounting is a mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee.See "Time Value", "Discount", "Discount Yield", "Compound Interest", "Effic ...

computed from the interest rate ''r''. Complications are possible in various circumstances. For example, the

interest rate An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, ...

for discounting cash receipts might be greater than the interest rate for discounting expenditures, because future inflows may be borrowed against while currently available funds may be invested temporarily pending use for future expenditures, and borrowing rates may exceed investment returns.

Applications

In most applications, the entire budget would be used up, because any unspent funds would represent unobtained potential utility. In these situations, the intertemporal budget constraint is effectively an equality constraint. In an

intertemporal consumption Economic theories of intertemporal consumption seek to explain people's preferences in relation to consumption (economics), consumption and saving over the course of their lives. The earliest work on the subject was by Irving Fisher and Roy Harrod ...

model, the sum of utilities from expenditures made at various times in the future, these utilities discounted back to the present at the consumer's rate of

time preference In behavioral economics, time preference (or time discounting,. delay discounting, temporal discounting, long-term orientation) is the current relative valuation placed on receiving a good at an earlier date compared with receiving it at a late ...

, would be maximized with respect to the amounts ''x''_''t'' consumed in each period, subject to an intertemporal budget constraint. In a model of

intertemporal portfolio choice Intertemporal portfolio choice is the process of allocating one's investable wealth to various assets, especially financial assets, repeatedly over time, in such a way as to optimize some criterion. The set of asset proportions at any time defines ...

, the objective would be to maximize the

expected value In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informa ...

expected utility The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Ratio ...

of final period wealth. Since investment returns in each period generally would not be known in advance, the constraint effectively imposes a limit on the amount that can be invested in the final period—namely, whatever the wealth accumulated as of the end of the next-to-last period is.

Applications

See also