The becker time allocation model
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The individual labour supply framework operates with two commodities goods (bought with earned or unearned income) and leisure. The individuals level of utility can be derived from the utility function by taking a combination of goods and leisure. Individuals will always try to maximise utility, this can be done by finding the highest indifference curve that is tangential to the budget constraint, as shown below.
The consumption constraint (c1) show in Fig1 can be altered through a change in the market work wage rate, as the budget constraint slope is the wage rate. An alteration of this gradient is known as the substitution effect, where depending on whether the wage rate increases or decrease the individual will substitute either goods for leisure or leisure for goods. As the wage rate implicitly rises the individual will choose to substitute away from leisure activities and instead take part in more hours of market work. This move is shown by the budget constraint becoming steeper (BC2). The income effect now shifts the whole budget constraint up to (BC3), touching the indifference curve I2 increase. In the case drawn above the income effect is greater than that of the substitution effect as L to L1 (substitution effect) is less than L1 to L2 (income effect). If the substitution effect was to become dominant the point L2 on the graph would have to be shifted to the left of point L. This model is one of the simplest labour supply models where only one variable has been changed, it also only takes into account consumption and nothing that individual may do outside of market work.
Gary Becker changed the thinking on labour supply in 1965 with his paper on the model of time allocation. He suggested that households can produce goods as well as consume them, he also added time into the model, as all activities use a finite amount of time and households must choose how much time they devote to each activity. The main aspect of the time allocation models is the production possibilities frontier of the household. Fig2 below shows what the production possibility curve looks like in its simplest form.
The household production possibility frontier is represented by the line abc in fig2, from a to point b the household takes part in non-market work as the return is greater than that of market work. This changes at point T as the household can obtain more goods working in market work than non-market for the same amount of time, the wage rate is constant for any market hours in this case therefore any hours of market work will return more goods than any extra hours of non-market work. This model is good for showing the basic features of household production however it needs to be advanced to include indifference curves and what changes in wage rates would do to change the production possibilities frontier.
When leisure is also factored into the model indifference maps need to be drawn up to show the combination of work and leisure most preferable to the individual. In the diagram the individual may have a higher preference for leisure, this will mean the individual will not want to work any market hours but instead work in the home. It's only if the individual has a high preference for goods instead of leisure that they would engage in market work to obtain the higher level of goods through earned income. If there was however a wage rate increase the individual who had a high preference for goods could increase their consumption even more. Ia would shift to I1a meaning the individual could obtain higher goods for less market work time. This diagram is still not a perfect way to explain labour supply as it does not say how much time is actually split between household work and leisure.
Becker's approach differs slightly in that he says all activities involve an input of time. Not only do all activities involve time but each activity differs in the amount of time it takes to do. For example cricket is a very time intensive activity where as a drink at the pub is a relatively low time intensive activity. Becker sees that foregone earnings a more important to economic analysis than different length of time and types of leisure arguments. This is mainly due to the difficulty in defining the difference between a leisure activity and a non-work activity. For example child care can be classed as leisure as well as household production activity. Perhaps even more difficult to define would be commuting, as it is essential to participate in market work in most cases however it is part of working hours so could be classed as a non-work activity. Therefore thinking of these activities in the sense of how much income is lost form partaking in them is a much better way of thinking about why individuals choose to do certain activities. With this in mind Becker finds a rise in earnings would increase the cost of activities with large forgone earnings, this would make individuals substitute away from these activities and instead increase the number of hours employed in market work. He also suggests that that a fall in the costs of the activities would also induce a substitution away from the activities and increase the number of hours employed in market work.
The productivity of time at work and time in leisure and non-work activities is important for analysing why working hours have decreased and leisure hours have increased. The constant increase in earnings has been largely due to increased wage rates due to improved productivity in the work place. This in part is due to technological progress, increased labour productivity and physical capital. The increased productivity in working time produces a income affect greater than the substitution affect. The increased productivity in consumption time has done the opposite the income and substitution affect, with substitution affect being greater than the income affect. Becker (1965) believes the income affect will be greater overall taking into account both consumption and work productivity increase, this is due to two income affects occurring .The number of hours worked by men is seen to decline less as income increases than women. Becker (1965) explains that this is due to the relationship between income and hours work being negatively related but at a shallower rate than before. This suggests that the substitution effect for men is very strong and the income effect is weak.
Becker also analysed the effect that a wage rate rise would have on the transportation costs for travelling to and from work. As the earned income rises the cost of commuting also increases, as the time spent commuting has a higher forgone income cost. This differs from the traditional view that as income rises individuals are more willing to travel longer distances to work, with this though individuals will also want better housing. So under Becker's model suggests that the rise in income will mean the commuting cost will conflict with the housing demand, it will be whichever is more important to the individual that will determine the equilibrium level of amount of commuting and housing space.
The importance of how the family as a unit take part in labour supply model is not focused on by Becker in great detail. He does however suggest that families will divide activities amongst themselves according to how appropriate they are at doing those activities. "The allocation of time of any member is greatly influenced by the opportunities open to other members". This suggests that if a member becomes more efficient in market work then others would reallocate their time to allow the member to engage in market work. A more in-depth analysis of this concept can be found in Shelly Lundberg and Robert A. Pollack's journal on The American Family and Family economics. They observed that families have become more heterogeneous and more prone to change their structure, this has meant analysis of them has become increasingly difficult. It has been widely observed that gender specialisation in the work task's at home and in market work have been reduced dramatically. Women are no longer wanting to stay at home and provide for a family, instead many have careers and don't worry about getting married to have a family unit. Being part of a family is just less important than it has been, mainly due to functions provided by the family like child care are now provided for by the state at a basic level. There are many articles on why the family unit has decreased in size and importance, but nearly all of them focus on the increase in earnings. The rest put emphasis on the changing social environment we live in. The national statistics suggest that 70% of women now participate in labour market compared to only 56% in 1971, this proves that women are now more interested in paid work. The pay gap between men and women has also decreased, women now earn 86% of what men earn. This could suggest that the overall market wage increases over the past 50 years has persuaded women to pursue a career and put less importance on having a family. This all links in with Becker's 1965 model, that household activities will be divided up between so that the most efficient level of production is achieved.
Moving on from Becker's time allocation theory Gronau issued a paper in 1977 revising Becker's ideas on the subject. Becker's model misses out a lot of information about household production, mainly how to distinguish between work at home and leisure. This is in part due to the difficulties of distinguishing between the two seemed to stop people from investigating household production. The main aim of (Gronau 1977) is to find how the family allocates its time within the home. (Gronau 1976) and (Bloch 1973) both did studies into the what affects a man or woman's allocation of time between household work, leisure and market work. Gronau and Bloch both found that children will cause the mother to transfer time from market work to household work but also reduce her leisure time. The father instead increases hours in market work and in household work, this is done with a reduction in leisure hours.
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