Intertemporal choice

Intertemporal choice is the process by which people make decisions about what and how much to do at various points in time, when choices at one time influence the possibilities available at other points in time. These choices are influenced by the relative value people assign to two or more payoffs at different points in time. Most choices require decision-makers to trade off costs and benefits at different points in time. These decisions may be about saving, work effort, education, nutrition, exercise, health care and so forth. Intertemporal choice is the process by which people make decisions about what and how much to do at various points in time, when choices at one time influence the possibilities available at other points in time. These choices are influenced by the relative value people assign to two or more payoffs at different points in time. Most choices require decision-makers to trade off costs and benefits at different points in time. These decisions may be about saving, work effort, education, nutrition, exercise, health care and so forth. Since early in the twentieth century, economists have analyzed intertemporal decisions using the discounted utility model, which assumes that people evaluate the pleasures and pains resulting from a decision in much the same way that financial markets evaluate losses and gains, exponentially 'discounting' the value of outcomes according to how delayed they are in time. Discounted utility has been used to describe how people actually make intertemporal choices and it has been used as a tool for public policy. Policy decisions about how much to spend on research and development, health and education all depend on the discount rate used to analyze the decision. Intertemporal portfolio choice is the allocation of funds to various assets repeatedly over time, with the amount of investable funds at any future time depending on the portfolio returns at any prior time. Thus the future decisions may depend on the results of current decisions. In general this dependence on prior decisions implies that current decisions must take into account their probabilistic effect on future portfolio constraints. There are some exceptions to this, however: with a logarithmic utility function, or with a HARA utility function and serial independence of returns, it is optimal to act with (rational) myopia, ignoring the effects of current decisions on the future decisions. The Keynesian consumption function was based on two major hypotheses. Firstly, the marginal propensity to consume lies between 0 and 1. Secondly, the average propensity to consume falls as income rises. Early empirical studies were consistent with these hypotheses. However, after World War II it was observed that saving did not rise as income rose. The Keynesian model therefore failed to explain the consumption phenomenon, and thus the theory of intertemporal choice was developed. The analysis of 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. A few other models based on intertemporal choice include the Life Cycle Income Hypothesis proposed by Franco Modigliani and the Permanent Income Hypothesis proposed by Milton Friedman. The concept of Walrasian equilibrium may also be extended to incorporate intertemporal choice. The Walrasian analysis of such an equilibrium introduces two 'new' concepts of prices: futures prices and spot prices. Irving Fisher developed the theory of intertemporal choice in his book Theory of interest (1930). Contrary to Keynes, who related consumption to current income, Fisher's model showed how rational forward looking consumers choose consumption for the present and future to maximize their lifetime satisfaction. According to Fisher, an individual's impatience depends on four characteristics of his income stream: the size, the time shape, the composition and risk. Besides this, foresight, self-control, habit, expectation of life, and bequest motive (or concern for lives of others) are the five personal factors that determine a person's impatience which in turn determines his time preference. In order to understand the choice exercised by a consumer across different periods of time we take consumption in one period as a composite commodity. Suppose there is one consumer, N {displaystyle N} commodities, and two periods. Preferences are given by U ( x 1 , x 2 ) {displaystyle U(x_{1},x_{2})} where x t = ( x t 1 , … , x t N ) {displaystyle x_{t}=(x_{t1},dots ,x_{tN})} . Income in period t {displaystyle t} is Y t {displaystyle Y_{t}} . Savings in period 1 is S 1 {displaystyle S_{1}} , spending in period t {displaystyle t} is C t {displaystyle C_{t}} , and r {displaystyle r} is the interest rate. If the person is unable to borrow against future income in the first period, then he is subject to separate budget constraints in each period: On the other hand, if such borrowing is possible then the person is subject to a single intertemporal budget constraint: The left hand side shows the present value of expenditure and right hand side depicts the present value of income. Multiplying the equation by ( 1 + r ) {displaystyle (1+r)} would give us the corresponding future values.