Introduction to A Theory of the Allocation of Time by Gary Becker.

Gary Becker's classic study, ‘A theory of the allocation of time’, laid the analytical foundations for the study of household production and the allocation of time within the household. It spawned a large literature and continues to influence economics and other social sciences.

The article was written when Becker was in his mid-30s, teaching at Columbia University and conducting research at the National Bureau of Economic Research, then headquartered in New York. Over the period 1958–69, Becker, along with Jacob Mincer, organised the legendary Columbia Labour Economics Workshop. Becker, Mincer and their students applied price theory to study the economics of fertility, labour supply, income inequality, education, on-the-job training, crime and punishment and the theory of irrational behaviour, among other topics. The interplay between theory and data was the hallmark of that group. From this crucible emerged the modern theory of human capital (Becker, ,) and important components of the modern economics of the family that were distilled and extended in Becker's classic A Treatise on the Family (1981, enlarged in 1991). A generation of productive and influential scholars was trained at Columbia during this period (Heckman, 2014).

In his introduction to this article, Becker discusses the body of research on the economics of time that was being conducted at Columbia, to which he contributed and from which he had drawn. This article is the analytical synthesis of a body of ideas developed in that intense intellectual climate.

Many scholars have tried to disentangle the contributions of Jacob Mincer from those of Gary Becker during the period of their synergistic collaboration. Attempts to do so miss the highly interactive and mutually supportive intellectual environment of the Columbia group and the ability of Becker to create clean analytical insights from diverse bodies of empirical work and to stimulate all those around him.

1. Some Background on This Article

Prior to the work of Becker, the household had a shadowy place in analytical economics. Mitchell (1912) wrote about the ‘backward art of spending money’ and compared the efficiency of firms in producing goods for the market to the inefficiency of households in producing domestic services. Kuznets (1934) lamented that GNP accounts omitted important components of household production.1 Reid (1934) wrote a textbook on home production aimed at students of home economics. It offered practical advice, sketched some analytical principles and offered interesting speculation about the future of the household and the role of women.2

It was not until the work of Becker (1965) that economists began to model households formally as engaged in activities producing outputs such as food, children and housing (the for commodity i in his article) that bundled goods and time. The household consumed these commodities as the direct objects of utility.3 The outputs of the activities were produced by distinct inputs.4 The commodities were associated with consumption in different time periods (Ghez and Becker, 1975) or production of different activities (meals, health, housing, child rearing) as in Becker (1965), Muth (1966), Grossman (1972a, b) and Michael (1972, 1973).5 Becker and Mincer breathed empirical life into these models and spawned a large literature (Gronau, ,,,,; Grossman, 1972a, b; Michael, 1973, 1974; Michael and Becker, 1973; Leibowitz, 1974; Rosenzweig and Schultz, 1983; Juster and Stafford, ,; Pollak, 2003).

The Becker–Mincer research on human capital (Mincer, 1958, 1962a, 1974; Becker, ,,) emphasised the importance of time foregone from earnings as the primary cost of education and job training, far more important than costs arising from tuition or fees. In other work, Mincer (1962b, 1963) made a major contribution to empirical research on the labour supply of women by isolating the effects of wages (the price of time) from pure income effects, explaining both the cross-section and time series of married female labour supply.6

While Robbins (1930) had previously distinguished income effects from substitution effects in labour supply, the empirical literature on female labour supply had not made this distinction. Long (1958), in an extensive empirical study, emphasised the role of consumer durables in releasing female time from housework for market uses but did not study the effects of wages on labour supply.7 In a similar spirit, Becker's (1960) early work on fertility focused on income effects and did not discuss the importance of female time and its price in explaining fertility.8 It was Mincer who first emphasised the role of the rise in the wage of women as a primary force explaining the growth of female labour supply.

Mincer (1962b) introduced another feature of household production that is formalised in Becker (1965). Mincer claimed that the multiple uses of non-market time (in child care and other household activities) produced a greater wage elasticity for women than for men because they faced more margins of substitution. While formally this argument is incorrect, the intuition behind it is powerful and continues to shape thinking about female labour supply (Heckman, 1988).

2. The Becker Model

The household is assumed to produce and consume a vector of commodities . These commodities are associated with different levels of activities performed by the household (e.g. consumption of food, child-rearing, leisure activities), including leisure on the job (Juster and Stafford, 1985; Aguiar and Hurst, 2007; Aguiar et al., 2012). Utility is a function of these commodities:

where

is a vector of goods used to produce and is time (usually assumed scalar but allowed to be a vector in Becker, 1965).9 The price of depends on the prices of its components. Assuming that each is homogeneous of degree 1, one can construct a scale-invariant price index for each commodity.

The household faces both time and traditional budget constraints. Using elementary algebra, Becker shows that under his assumptions the household effectively faces one constraint.10 Under the assumption that is scalar, and that the price of time is w across all uses, the maximum amount of income that the person can earn is full income B = wT + V where and V is the amount of unearned income accruing to the household. The encompass all activities in which time can be used (including the consumption of leisure on the job) and

The household is assumed to maximise (1) subject to (2) and (3). The demands for inputs , are derived from the demands for . The responsiveness of the demands for different activities in response to changes in the prices of goods and time depends, in part, on the time and goods intensities in producing the commodities. Becker goes on to develop a more general analysis where the marginal cost of time varies across activities.

Becker's model of commodity demand is an instance of Gorman's (1959) general separability analysis where U is weakly separable in the arguments producing the , and the are homogeneous of degree 1.11 Under homogeneous weak separability, consumer decision making can be characterised by a two stage budgeting process. Agents allocate budgets to each commodity i, based on the price index and in a second stage maximise each subject to these allocations determined from the first stage to determine and (Strotz, 1957; Gorman, 1959).12 Pollak and Wachter (1975) present a definitive analysis of the limitations of the Becker model when the assumption of homogeneous separability is relaxed and when joint production is considered.13 See also the discussion in Gronau (1977, 1986).14

3. Its Influence

Although others had developed analytical frameworks with similar features, Becker's great contribution was to apply the model to interpret a broad array of empirical phenomena and to inspire the generations that followed in his wake to investigate the economics of home production. The concept of non-market production of human capital (Ben-Porath, 1967), children (Becker and Lewis, 1973; Willis, 1973), health (Grossman, 1972a,b; Becker, 2007b), the value of life (Viscusi and Aldy, 2003), the production of child quality (Leibowitz, 1974; Cunha and Heckman, 2007), transportation (Gronau, 1970), the consumption of leisure on-the-job ( Juster and Stafford, 1985; Aguiar and Hurst, 2007; Aguiar et al., 2012) are just a few of the numerous applications of these ideas.15 Becker's article also stimulated the collection of data on time use in household production ( Juster and Stafford, ,; Aguiar et al., 2012).

4. Theory of Labour Supply

When Becker's article was initially published, many scholars noted that under the assumption that the price of time was uniform across alternative uses, application of Hicks's composite commodity theorem (Hicks, 1939) leads back to the elementary analysis of labour supply by Lionel Robbins. All non-market time can be aggregated into a single composite ‘leisure’ (Heckman, 1988). There was no need for household production theory to analyse the supply of labour to the market.

While formally true, this commentary misses several key points. First, Becker analysed a situation in which the marginal prices of time may differ in different uses.16 Second, his article reconciled the Long (1958) interpretation of the growth of the labour supply of women as arising from a shift in the supply of labour through the introduction of labour-saving consumer durables, and the model favoured by Mincer (1962b) that shifts in the demand for female labour led to higher wages and higher labour supply (Greenwood et al., 2005).

More generally, Becker's framework allowed for a deeper understanding of the mechanisms of consumer choice, and interpretation of income and substitution effects. Its continuing relevance to empirical economics is a testimony to its power.

5. Developments After This Article

Becker was near the beginning of his long and productive career when he wrote this article. He elaborated the model in his later work. However, the analytical framework of household production theory developed in this article remained a pillar of his later work on the economics of the family and the economics of non-market activities more generally.

He devotes only one paragraph of this article to the idea that household members might specialise in the production of commodities. He developed it much further in Becker (1973, 1974, 1981, 1991). There he developed theories of household formation and marital sorting and investigated the consequences of intrahousehold specialisation in tasks for life cycle earnings and productivity.17 For a recent exposition of the development of these themes, see Browning et al. (2014).