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Households are suppliers of labour. In microeconomics theory, people are assumed rational and seeking to maximize their utility function. In this labour market model, their utility function is determined by the choice between income and leisure. However, they are constrained by the waking hours available to them.
Let w denote hourly wage. Let k denote total waking hours. Let L denote working hours. Let π denote other incomes or benefits. Let A denote leisure hours.The utility function and budget constraint can be expressed as following:
This can be shown in a diagram (below) that illustrates the trade-off between allocating your time between leisure activities and income generating activities. The linear constraint line indicates that there are only 24 hours in a day, and individuals must choose how much of this time to allocate to leisure activities and how much to working. (If multiple days are being considered the maximum number of hours that could be allocated towards leisure or work is about 16 — Everyone has to sleep eventually!) This allocation decision is informed by the curved indifference curveIn microeconomics, an indifference curve is a graph showing combinations of two goods to which an economic agent (such as a consumer or firm) is indifferent that is, it has no preference for one combination over the other. They are used to analyse the cho labeled IC. The curve indicates the combinations of leisure and work that will give the individual a specific level of utility. The point where the highest indifference curve is just tangent to the constraint line (point A), illustrates the short-run equilibrium for this supplier of labour services.
If the preference for consumption is measured by the value of income obtained, rather than work hours, this diagram can be used to show a variety of interesting effects. This is because the slope of the budget constraint becomes the wage rate. The point of optimization (point A) reflects the equivalency between the wage rate and the marginal rate of substitutionIn economics, the marginal rate of substitution is the rate at which consumers are willing to give up one good in exchange for more units of another good. Numerically, this is the negative slope or derivative (evaluated at a point) of the indifference cur, leisure for income (the slope of the indifference curve). Because the marginal rate of substitution, leisure for income, is also the ratio of the marginal utility of leisure (MUL) to the marginal utility of income (MUY), one can conclude:
If wages increase, this individual's constraint line pivots up from X,Y1 to X,Y2. He/she can now purchase more goods and services. His/her utility will increase from point A on IC1 to point B on IC2. To understand what effect this might have on the decision of how many hours to work, you must look at the income effect and substitution effect.
The wage increase shown in the previous diagram can be decompiled into two separate effects. The pure income effect is shown as the movement from point A to point C in the next diagram. Consumption increases from YA to YC and — assuming leisure is a normal good — leisure time increases from XA to XC (employment time decreases by the same amount; XA to XC).
But that is only part of the picture. As the wage rate rises, the worker will substitute work hours for leisure hours, that is, will work more hours to take advantage of the higher wage rate, or in other words substitute away from leisure because of its higher opportunity costOpportunity cost is a term used in economics, to mean the cost of something in terms of an opportunity foregone (and the benefits that could be received from that opportunity), or the most valuable forgone alternative''. For example, if a city decides to. This substitution effect is represented by the shift from point C to point B. The net impact of these two effects is shown by the shift from point A to point B. The relative magnitude of the two effects depends on the circumstances. In some cases the substitution effect is greater than the income effect (in which case more time will be allocated to working), but in other cases the income effect will be greater than the substitution effect (in which case less time is allocated to working). The intuition behind this latter case is that the worker has reached the point where his marginal utilityIn economics, marginal utility is the additional utility (satisfaction or benefit) that a consumer derives from an additional unit of a commodity or service. The concept grew out of attempts by 19th-century economists to explain the fundamental economic r of leisure outweighs his marginal utility of income. To put it in less formal (and less accurate) terms: there is no point in earning more money if you don't have the time to spend it.
If the substitution effect is greater than the income effect, the supply of labour curve (diagram to the left) will slope upwards to the right, as it does at point E for example. This individual will continue to increase his supply of labour services as the wage rate increases up to point F where he is working HF hours (each period of time). Beyond this point he will start to reduce the amount of labour hours he supplies (for example at point G he has reduced his work hours to HG). Where the supply curve is sloping upwards to the right (positive wage elasticity of labour supply), the substitution effect is greater than the income effect. Where it slopes upwards to the left (negative elasticity), the income effect is greater than the substitution effect. The direction of slope may change more than once for some individuals, and the labour supply curve is likely to be different for different individuals.
Other variables that affect this decision include taxation, welfare, and work environment.
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