Utility Maximisation Subject to Income and Time Constraints The consumption of economic goods often takes time. Consider, for example:


Transport services, eg flights, rail journeys;
Leisure goods, eg watching a film, visiting a park.


I would like to explore models of consumer or household behaviour in which utility in a period is maximised subject to both income and time constraints. 

From a Google search, two important (but rather old) papers on this topic appear to be:


Becker, G S (1965) A Theory of the Allocation of Time
De Serpa, A C (1971) A Theory of the Economics of Time


What are other (and more recent) key papers on this topic?

Addendum 31 May 2018

To give a simple example, suppose there are just two goods $X_1,X_2$ and utility $U$ is given by:

$$U = X_1^{0.5}X_2^{0.5}$$

Suppose further that the respective prices and time requirements are for $X_1 (1,2)$ and for $X_2 (2,1)$.  Thus the income and time constraints are:

$$X_1 + 2X_2 \leq I$$

$$2X_1 + X_2 \leq T$$

where $I$ is income and $T$ is available time. If $T$ is much larger than $I$ (low-income person), then the income constraint will be binding, and the time constraint will be slack, and vice versa if $I$ is much larger than $T$ (high-income person). Over an intermediate range, including $T = I$, both constraints will be binding. These different scenarios have different implications for the effect of a marginal change in price.  Perhaps time preference is relevant here but I can't immediately see how.

Addendum 23 July 2018

This book by Ian Steedman, reviewed here by Diane Coyle, looks relevant.
Despite its funny title and although it is quite old you may find this paper interesting:

The economics of the afterlife by Scott Gordon in the JPE. His argument is basically that in the presence of an infinite amount of time there would still be a rate of time preference.

A follow-up paper disproving Gordon's claim was written by Amegashie, but I haven't checked that one in detail. You can find that  here.

Nb credit where credit is due: I would probably never have read the first paper without Yoram Bauman's presentation "Hyperinflation in hell"