Editing Labour economics (section)

===Neoclassical supply===

{{See also|Labour supply}}
[[File:Tompkins Square Park Central Knoll.jpg|thumb|right|The neoclassical model analyzes the trade-off between leisure hours and working hours.]]
[[File:RAILROAD WORK CREW IMPROVES THE TRACKS AND BED OF THE ATCHISON, TOPEKA AND SANTA FE RAILROAD NEAR BELLEFONT, KANSAS... - NARA - 556012.jpg|thumb|right|Railroad work]]

Households are suppliers of labour. In microeconomic theory, people are assumed to be rational and seeking to maximize their [[utility function]]. In the labour market model, their utility function expresses trade-offs in preference between leisure time and income from time used for labour. However, they are constrained by the hours available to them.

Let ''w'' denote the hourly wage, ''k'' denote total hours available for labour and leisure, ''L'' denote the chosen number of working hours, π denote income from non-labour sources, and ''A'' denote leisure hours chosen. The individual's problem is to maximise utility ''U'', which depends on total income available for spending on consumption and also depends on the time spent in leisure, subject to a time constraint, with respect to the choices of labour time and leisure time:

:<math>\text{maximise} \quad U(wL + \pi, A) \quad \text{subject to} \quad L + A \le k </math>

This is shown in the graph below, which illustrates the trade-off between allocating time to leisure activities and allocating it to income-generating activities. The linear constraint indicates that every additional hour of leisure undertaken requires the loss of an hour of labour and thus of the fixed amount of goods that that labour's income could purchase. Individuals must choose how much time to allocate to [[leisure]] activities and how much to [[wage labour|working]]. This allocation decision is informed by the [[indifference curve]] labelled IC<sub>1</sub>. 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 optimum for this supplier of labour services.

If consumption is measured by the value of income obtained, this diagram can be used to show a variety of interesting effects. This is because the absolute value of the slope of the budget constraint is the wage rate. The point of optimisation (point A) reflects the equivalency between the wage rate and the [[marginal rate of substitution]]<ref name="robertfrank">{{cite book|url=http://students.aiu.edu/submissions/profiles/resources/onlineBook/P3w4i7_Frank-Microeconomics-and-Behavior.pdf|access-date=January 26, 2023|title=Microeconomics and Behavior|last=Frank|first=Robert H.|author-link=Robert H. Frank|edition=Seventh|publisher=[[McGraw Hill Education|McGraw Hill]]/Irwin|isbn=978-0-07-337573-1|year=2008}}</ref> of leisure for income (the absolute value of the slope of the indifference curve). Because the marginal rate of substitution of leisure for income is also the ratio of the [[marginal utility]] of leisure (MU<sup>L</sup>) to the marginal utility of income (MU<sup>Y</sup>), one can conclude:

:<math>{{MU^L}\over{MU^Y}} = {{dY}\over{dL}},</math>

where ''Y'' is total income and the right side is the wage rate.

<div style="float:center;text-align:center">
[[File:Labour wage increase small.png|class=skin-invert-image|Effects of a wage increase]]<br />''Effects of a wage increase''</div>
If the wage rate increases, this individual's constraint line pivots up from X,Y<sub>1</sub> to X,Y<sub>2</sub>. He/she can now purchase more goods and services. His/her utility will increase from point A on IC<sub>1</sub> to point B on IC<sub>2</sub>.
To understand what effect this might have on the decision of how many hours to work, one must look at the [[income effect]] and [[substitution effect]].

The wage increase shown in the previous diagram can be decomposed 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 Y<sub>A</sub> to Y<sub>C</sub> and – since the diagram assumes that leisure is a [[normal good]] – leisure time increases from X<sub>A</sub> to X<sub>C</sub>. (Employment time decreases by the same amount as leisure increases.)

<div style="float:center;text-align:center">[[File:Labour supply income and substitution effects small.png|class=skin-invert-image|The Income and Substitution effects of a wage increase]]<br />''The Income and Substitution effects of a wage increase''</div>

But that is only part of the picture. As the wage rate rises, the worker will substitute away from leisure and into the provision of labour—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 cost]]. 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, such as the one shown, 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 individual decides that the higher earnings on the previous amount of labour can be "spent" by purchasing more leisure.

<div style="float:left;text-align:center">[[File:Labour supply small.png|class=skin-invert-image|The Labour Supply curve]]<br />''The Labour Supply curve''</div>

If the substitution effect is greater than the income effect, an individual's supply of labour services will increase as the wage rate rises, which is represented by a positive slope in the '''labour supply curve''' (as at point E in the adjacent diagram, which exhibits a positive wage [[Elasticity (economics)|elasticity]]). This positive relationship is increasing until point F, beyond which the income effect dominates the substitution effect and the individual starts to reduce the number of labour hours he supplies (point G) as wage increases; in other words, the wage elasticity is now negative.

The direction of the slope may change more than once for some individuals, and the labour supply curve is different for different individuals.

Other variables that affect the labour supply decision, and can be readily incorporated into the model, include taxation, welfare, work environment, and income as a [[Signalling (economics)|signal]] of ability or social contribution.