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Intertemporal choice is the study of the relative value people assign to two or more payoffs at different points in time. This relationship is usually simplified to today and some future date. Intertemporal choice was introduced by John Rae in 1834 in the "Sociological Theory of Capital". Later, Eugen von Böhm-Bawerk in 1889 and Irving Fisher in 1930 elaborated on the model.
According to this model there are three types of consumption: past, present and future.
When making decisions between present and future consumption, the consumer takes his/her previous consumption into account.
This decision making is based on an indifference map with negative slope because if he consumes something today it means that he can't consume it in the future and vice versa.
The revenue is in form of interest rate. Nominal interest rate - inflation = real interest rate
Denote
Then maximum present consumption is:
The maximum future consumption is:
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophers such as Jeremy Bentham and John Stuart Mill. The term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a utility function that represents a consumer's ordinal preferences over a choice set, but is not necessarily comparable across consumers or possessing a cardinal interpretation. This concept of utility is personal and based on choice rather than on pleasure received, and so requires fewer behavioral assumptions than the original concept.
The theory of consumer choice is the branch of microeconomics that relates preferences to consumption expenditures and to consumer demand curves. It analyzes how consumers maximize the desirability of their consumption, by maximizing utility subject to a consumer budget constraint. Factors influencing consumers' evaluation of the utility of goods include: income level, cultural factors, product information and physio-psychological factors.
In economics, time preference is the current relative valuation placed on receiving a good or some cash at an earlier date compared with receiving it at a later date.
In economics, a budget constraint represents all the combinations of goods and services that a consumer may purchase given current prices within his or her given income. Consumer theory uses the concepts of a budget constraint and a preference map as tools to examine the parameters of consumer choices. Both concepts have a ready graphical representation in the two-good case. The consumer can only purchase as much as their income will allow, hence they are constrained by their budget. The equation of a budget constraint is where is the price of good X, and is the price of good Y, and m is income.
Consumption is the act of using resources to satisfy current needs and wants. It is seen in contrast to investing, which is spending for acquisition of future income. Consumption is a major concept in economics and is also studied in many other social sciences.
In economics, hyperbolic discounting is a time-inconsistent model of delay discounting. It is one of the cornerstones of behavioral economics and its brain-basis is actively being studied by neuroeconomics researchers.
Utility maximization was first developed by utilitarian philosophers Jeremy Bentham and John Stuart Mill. In microeconomics, the utility maximization problem is the problem consumers face: "How should I spend my money in order to maximize my utility?" It is a type of optimal decision problem. It consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending (income), the prices of the goods and their preferences.
Economic theories of intertemporal consumption seek to explain people's preferences in relation to consumption and saving over the course of their lives. The earliest work on the subject was by Irving Fisher and Roy Harrod, who described 'hump saving', hypothesizing that savings would be highest in the middle years of a person's life as they saved for retirement.
A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the remaining decision problem that results from those initial choices. This breaks a dynamic optimization problem into a sequence of simpler subproblems, as Bellman's “principle of optimality" prescribes. The equation applies to algebraic structures with a total ordering; for algebraic structures with a partial ordering, the generic Bellman's equation can be used.
In economics, dynamic inconsistency or time inconsistency is a situation in which a decision-maker's preferences change over time in such a way that a preference can become inconsistent at another point in time. This can be thought of as there being many different "selves" within decision makers, with each "self" representing the decision-maker at a different point in time; the inconsistency occurs when not all preferences are aligned.
In economics, discounted utility is the utility (desirability) of some future event, such as consuming a certain amount of a good, as perceived at the present time as opposed to at the time of its occurrence. It is calculated as the present discounted value of future utility, and for people with time preference for sooner rather than later gratification, it is less than the future utility. The utility of an event x occurring at future time t under utility function u, discounted back to the present using discount factor Is
The permanent income hypothesis (PIH) is a model in the field of economics to explain the formation of consumption patterns. It suggests consumption patterns are formed from future expectations and consumption smoothing. The theory was developed by Milton Friedman and published in his A Theory of Consumption Function, published in 1957 and subsequently formalized by Robert Hall in a rational expectations model. Originally applied to consumption and income, the process of future expectations is thought to influence other phenomena. In its simplest form, the hypothesis states changes in permanent income, rather than changes in temporary income, are what drive changes in consumption.
Consumption smoothing is an economic concept for the practice of optimizing a person's standard of living through an appropriate balance between savings and consumption over time. An optimal consumption rate should be relatively similar at each stage of a person's life rather than fluctuate wildly. Luxurious consumption at an old age does not compensate for an impoverished existence at other stages in one's life.
In economics, the absolute income hypothesis concerns how a consumer divides their disposable income between consumption and saving. It is part of the theory of consumption proposed by economist John Maynard Keynes. The hypothesis was subject to further research in the 1960s and 70s, most notably by American economist James Tobin (1918–2002).
In economics, elasticity of intertemporal substitution is a measure of responsiveness of the growth rate of consumption to the real interest rate. If the real interest rate rises, current consumption may decrease due to increased return on savings; but current consumption may also increase as the household decides to consume more immediately, as it is feeling richer. The net effect on current consumption is the elasticity of intertemporal substitution.
In consumer theory, a consumer's preferences are called homothetic if they can be represented by a utility function which is homogeneous of degree 1. For example, in an economy with two goods , homothetic preferences can be represented by a utility function that has the following property: for every :
A borrowing limit is the amount of money that individuals could borrow from other individuals, firms, banks or governments. There are many types of borrowing limits, and a natural borrowing limit is one specific type of borrowing limit among those. When individuals are said to face the natural borrowing limit, it implies they are allowed to borrow up to the sum of all their future incomes. A natural debt limit and a natural borrowing constraint are other ways to refer to the natural borrowing limit.
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 a portfolio. Since the returns on almost all assets are not fully predictable, the criterion has to take financial risk into account. Typically the criterion is the expected value of some concave function of the value of the portfolio after a certain number of time periods—that is, the expected utility of final wealth. Alternatively, it may be a function of the various levels of goods and services consumption that are attained by withdrawing some funds from the portfolio after each time period.
In economics and finance, an intertemporal budget constraint is a constraint faced by a decision maker 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 of current and future cash outflows cannot exceed the present value of currently available funds and future cash inflows. Typically this is expressed as
In macroeconomics, the Keynes–Ramsey rule is a necessary condition for the optimality of intertemporal consumption choice. Usually it is expressed as a differential equation relating the rate of change of consumption with interest rates, time preference, and (intertemporal) elasticity of substitution. If derived from a basic Ramsey–Cass–Koopmans model, the Keynes–Ramsey rule may look like
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