Abstract
Time-saving goods are defined as market goods that reduce home labor requirements (e.g., restaurants; washing machines). Assuming that time savings are costly, this paper shows that lower income individuals can purchase fewer time savings and enjoy less leisure time. Commodity tax rates affecting low-income individuals should depend more on time savings, and less on the classic Corlett and Hague rule. The related literature suggests to impose lower tax rates on goods that require less home labor. This paper shows that goods that offer greater time savings with respect to their more affordable substitutes should also receive favorable tax treatment.
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Notes
The term ‘commodity’ is commonly used in the optimal taxation literature to refer to any final market good and service, with or without time requirements. Following Becker (1965), in this paper the term ‘basic commodity’ denotes an activity that results from combining market goods or services with the time required to use them.
Time-saving goods that reduce production time include ‘labor-saving durable goods’ (e.g., washing machines, vacuum cleaners, dryers, electric irons, refrigerators), and ‘labor-saving household products and services’ (e.g., frozen or take-out foods and ready-made clothes) used by Greenwood et al. (2005) to explain the technological advances that allowed women to increase their labor force participation over the last century.
The effect of time savings on leisure and market labor can be considered as a mechanical component of the traditional income effect. In this case, income affects leisure and market labor not just through preferences, but also has a (necessarily) positive effect on the two variables through its influence on the time constraint.
Homothetic preferences for market goods imply that spending on each market good increases proportionally with the level of income, but this cannot happen if some goods are replaced by others. Since goods that provide more time savings are replacing those providing less time savings as income increases, we know that there are inferior and normal goods and thus preferences cannot be homothetic. In addition, the time-saving attribute of a good implies that its consumption can have a direct effect on leisure and thus preferences cannot, in general, be weakly separable between goods and leisure.
This definition corresponds to the concept of “full leisure” used by Boadway and Gahvari (2006), equal to the sum of pure leisure and the time used consuming perfect leisure-substitutes.
As explained, Greenwood et al. (2005) distinguish between ‘labor-saving durable goods’, like washing machines and vacuum cleaners, and ‘labor-saving household products and services’ like frozen pizza and take-out foods, which save the time spent in the activity “cooking.” Other market goods offer qualitative improvements that save time. A cleaner, for instance, is said to be of better quality if, other things equal, it requires less time to remove a stain. Luxury cars are examples of market goods that offer enjoyable improvements, which may allow to transform the home labor time used in transportation into leisure time.
Strictly speaking, given that all market goods require some labor to be produced, they can all be considered to save time. Even the market good “food,” for instance, saves the individual the time required to produce or collect food on her own.
As explained, even the time used on driving to the restaurant could be “saved” if this activity is made enjoyable, for instance, with a luxury car. This improvement, of course, affects only the price of the car, not the price of the dinner at the restaurant. For the purpose of the analysis, however, a market good might be assumed to be a good that integrates all time savings accumulated in the overall experience of going to the restaurant.
See Kleven (2004) and Boadway and Gahvari (2006) for examples of how home production is modeled in the optimal taxation literature. An alternative approach can be found in Gronau (1977), who uses a more general production function and assumes perfect substitutability between goods produced at home and goods purchased in the market.
Note that the time saved by improvements that make consumption time enjoyable, which provides no additional time available for production, is implicitly assumed to be exchanged with equal amounts of time spend on “pure leisure,” such that “full leisure” \( \rho \) (as defined by Boadway and Gahvari 2006), remains unchanged.
From this definition of the full price of \( z \) it is possible to derive alternative expressions provided in the literature, where it is commonly assumed that a market good \( x \) and \( \sigma \) are used in fixed proportions, but where there is no account for possible benefits and costs of time savings. For instance, Boadway and Gahvari (2006) define a as the fixed amount of time required to consume one unit of \( x \). Although they do not explicitly address the production problem, we can rewrite (2) to represent the framework implicitly used by them as \(z^{{\prime }} \left( {a,x_{n} } \right) = \hbox{min} \left\{ {ax_{n} ,x_{n} } \right\}\). This function leads to the optimal production condition \(ax_{n} = x_{n}\), which implies \( a=1 \). It is easy to see that the full price of \( x \) computed by Boadway and Gahvari (2006), \( p+wa \), is equivalent to the full price of z in the absence of time savings (\( \sigma_{s}=0 \)).
Related papers on optimal commodity taxation in the presence of home labor do not reach this conclusion because they are based on the assumption that each basic commodity \( z \) can be produced with only one market good that is combined with a fixed amount of home labor. Since substitution among market goods to produce the same \( z \) is disregarded, utility is maximized by allowing for substitution only among different basic commodities. The problem with the last approach is that it obscures the fact that a higher wage rate w allows to purchase more time savings and thus produce the same basic commodity with less home labor, increasing the ability of the individual to produce \( z \) and also to enjoy more leisure time.
Recall that by definition one unit of any market good \( x_{i} \) is used to produce one unit of \( z \), thus the amount of any market good used is necessarily equal to the production of basic commodity \( x_{i} = z \).
The new isoquant is no longer vertical when \(\sigma + \sigma_{s1} x_{1} \le x_{1}\); it has a slope equal to \( - 1/\sigma_{s}\) according to (3.a), and meets the vertical axis at \( h_{1} \). This is because the purchase of \( x_{1} \) is equivalent to an increase of \( x_{0} \) accompanied with additional time that further increases \( z \).
An increase in non-labor income makes additional time savings affordable and consequently may imply that it is optimal to use goods for which \(\pi_{i}>w\). For the sake of clarity, this case is disregarded and income is assumed to be obtained only from labor.
\( \pi \) must be lower than \( \pi_{n} \) because it corresponds to a weighted average of \( \pi_{n} \) and n − 1 smaller time-saving prices \( \pi_{i} \). Using the (discrete) notation of the previous section, \( \pi \) would be equivalent to \(\mathop \sum \nolimits_{i = 1}^{n} \pi_{i} \sigma_{si} /\sigma_{s}\).
Additional time-saving shares are expected to increase \( \pi \); however, given that prices \( \pi_{i} \) and total time-saving share \( \sigma_{s} \)(·) vary simultaneously and in the same direction, this assumption does not significantly affect the results of the model.
Boadway and Gahvari (2006) also allow for the full price of \( z \) to change with w, but do not account for the effect of w on time savings or, equivalently, on the home labor requirement of market goods.
The related concept of time poverty was introduced by Vickery (1977) to describe those cases where the time available for home production is below a predefined poverty threshold. This definition does not imply, however, that time poverty is related to income poverty. Recent discussions about time poverty can be found in Zacharias (2011), Antonopoulos et al. (2012) and Merz and Rathjen (2014).
A weekly income of $2884.61 is equivalent to an annual income of $150,411.81. As a reference, an individual annual income of $150,000 in the United States in 2018 corresponds, approximately, to the 94th percentile in the male population, and to the 98th percentile in the female population (Source: Current Population Survey (CPS) Annual Social and Economic (ASEC) Supplement; Bureau of Labor Statistics and Census Bureau).
Since most time variables are seemingly censored (with many zeros), it is natural to expect the Tobit model to provide unbiased estimates. However, Steward (2013) argued that the zeros are not due to censoring, but instead are explained by a mismatch between the period of the data (a day) and the period of interest (longer than a day), and showed that while Tobit estimates are biased, OLS estimates are not.
Note, however, that a change of \( \sigma_{sj} \) means that a different market good \( x_{j}\) is used to produce \( z_{j} \).
Kleven (2004) explicitly mentions market goods that “save time”; however, he does not introduce costly time savings in his model.
Of course, when marginal time savings per dollar are equal across goods, then the rule has no effect on optimal tax rates.
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Acknowledgements
I am grateful to Tuomas Matikka, Richard Weber and two anonymous referees for valuable comments and suggestions. I am also very grateful to Steven Sheffrin and James Alm for their support while I worked on this manuscript as part of my postdoctoral fellowship at the Murphy Institute at Tulane University.
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Sepulveda, C.F. Time-saving goods, time inequalities and optimal commodity taxation. Int Tax Public Finance 29, 84–109 (2022). https://doi.org/10.1007/s10797-020-09652-z
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DOI: https://doi.org/10.1007/s10797-020-09652-z