Intertemporal choice refers to the way in which a consumer’s current decisions influence the available options in the future. Thus, intertemporal choice denotes the study of relative value assigned to more than one payoff at varied instances in time. Majority of the consumption choices obliges decision-makers to trade-off expenses and gains at varied points in time. The principal component of intertemporal choices lies in the comprehension of the consumer-savings decisions made by consumers. This decision relies on tradeoffs, which consumers can encounter between the present and the future consumption periods (Deaton & Muellbauer 1994).
Buchanan (1976) cites the Ricardian equivalence theorem that postulates that under some given conditions, the deficit of the government’s budget remains irrelevant. To understand these decisions, it is imperative to put up a straightforward two-period-model of the economy, with such key variables as the actual rate of interest at which the government and consumers lend and borrow.
This paper supposes that consumers have two periods, present and the future. Over their existence, consumers receive income Yo presently and Yf in the future, which is affected by the tax rates per each period to and tf present and future tax rates respectively. The users must make sound choices about the quantity of the current consumption, Co, as well as the future’s consumption amount, Cf. Moreover, the user must choose the current savings, s, for carrying forward into the future, which can be included into future consumption. This paper further assumes that (1+r) denotes the gross savings’ return. With consumers’ income stream, everyone must choose three things- Co,S and Cf– throughout their existence.
Consumers encounter budget constraints in both the current and future periods. Simply put, this budget constraint implies that the consumer’s expenditures in each period can only be within his or her existing wealth. It is correct to argue that the consumer in this case (with two periods) faces two constraints, which can be written as follows:
Co+So=Yo-to (present) and
Cf=(1+r)So+Yf- tf (future)
Individual consumption behavior models start with the perception of a person maximizing satisfaction level (utility) from current consumption Co, and future consumption Cf. This could be represented as follows:
Max U= f(Co, Cf)
For a given consumer, this utility derived from consumption is discounted at ‘p’, which is the time preference rate, for future consumption. Higher amounts of this time preference rate mean lower fulfillment from the future consumption in comparison to the present consumption expenses. This pattern of consumption is restrained by the present Yo and future (expected) income levels, E[Yf]. the future income levels’ expectations, in this model, are founded on personal talents and skills, as well as possession of income generating resources Wo. Besides, patterns of consumption are constrained by ‘r’, the existing rates of interest that stands for aa reward or payment for preceding Co. Consequently, the two-period model will be denoted as:
Based on [Yp-Co] (1+r)+Wo=Cf-Yf
As aforementioned, the consumption of a given consumer should not surpass his or her wealth in any given period. Therefore, the consumer (in the first period) can only use the present income, while the second period has the future savings and savings brought forward from the previous period for consumption. Buchanan (1976) highlights that savings could either be positive or negative. This is illustrated in the following figures:
In case So<0, then the consumer borrowed to finance his or her higher consumption in the initial consumption phase. Therefore, this consumer shall pay back this loan in period two at an interest rate of (1+r), hence giving up some future consumption. On the contrary, if So>0, then the consumer made some savings in the first consumption phase in order to finance higher consumption in the future. Therefore, this consumer will receive their savings plus (1+r) gross return, and have a superior future consumption.