Introduction:

The Simple Work-Leisure Trade

off Model

The

income of any individual is related to the number of hours he or she works per

day and then per week. The net income is also related to per hour pay rate. If

the pay rate per hour is higher, then more income can be generated for fewer

working hours and more leisure hours. The leisure hours are those for which the

individual does not work and no income is generated in those hours. Therefore,

it can be said that the net income is related to the number of hours worked in

accordance with the pay rate per hour (Dean Garrat 2013). This study will

discuss the effects of working hours on the net income. Some assumptions are

made, such as:

·

No income is generated for

leisure hours (that is there is no savings for the individual or at least the

income from any saving or property, which is not to be included).

·

The reference point is one

single day.

·

The individual is free to chose

working hours per day (but it is very common that the individuals does not

chooses working hours by themselves, it is their employees who fix / expect

their workers to work for definite number of hours per week).

·

Any hours not considered as

working hours are assumed to be leisure hours.

As

mentioned earlier, there is a definite relationship between the net income

(wage) and the number of working hours. This relationship can be explained in

terms of plot between wage and working hours.

The

relationship is shown in figure where the number of hours has been taken along

x-axis and the money earned from work (wage) is shown on y axis. Working hour

is an independent variable and the wage earned is a dependant variable, because

the wage depends on number of hours worked per week.

Figure

1: Wage and work hours

There

are two budget constraints shown in figure 1, one for hourly wage rate of w1

(budget line 1 known as Bl1) and the second for an hourly rate of w2 (Bl2). It

is assumed that there are 24 working hours in a single day which means that the

number of leisure hours are zero. In total there are 24 working hours and that

is why both lines meet the x axis at 24 and Bl1 meets the y axis at 24w1

showing that for 24 working hours the wage will be 24w1. This can be calculated

for any given hourly rate, for instance if the hourly rate is £6.50 the total

earning will be £156 for 24 hours’ work.

Figure

2: Indifference curve for higher Figure

2: Indifference curve for lower satisfaction

satisfaction

level level

Budget

line 2 (Bl2) shows the line when hourly rate was increased from w1 to w2 where

w2 is larger than w1. This shows that if the hourly rate is increased then the

total wages would also increase for any given working hours as shown in figure

1.

In

figure 2 and figure 3 the examples of an indifference curves are shown where in

figure 2 the indifference curve is shown for an individual who not only enjoys

leisure but derives a lot of utility from the work associated with his job.

However, in figure 3 the indifference curve is shown for an individual who

enjoys leisure but derives much less utility from the work associated with the

job. In this case the curve is much closer to the axis. The utility function

measures the individual’s level of satisfaction or happiness. The higher the

level of satisfaction, the happier the person is. If the person is more

satisfied with his job and feels happier at work his utility index will be

larger and the indifference curve will be higher as shown in figure 2 (hks.harvard.edu).

Figure

4: Wage for changing work hours

The

indifference curves shown in figure 2 and 3 shows the way a particular worker

views the trade-off between leisure and consumption. Each graph represents the

way of work of each individual and different workers will typically view this

trade-off differently. This is understandable because some workers may like to

devote a great deal of time and effort to their jobs, whereas others would

prefer to devote most of their time to leisure. These interpersonal differences

in preferences imply that the indifference curves will certainly look quite

different based on individual’s behaviour (hks.harvard.edu).

In

figure 4 a single budget constraint w1 is shown for an hourly rate of £6.50 and

it assumed that the working hours are 6 hours per day. This shows that the

leisure hours will be 24 – 6 = 18 hours and that is why the budget constraint

line crosses the x axis at 18. In this case the total income for 6 hours’ of

work will be 6 x 6. 50 = £39.00. Due to this, the budget constraint line

crosses the y axis at 39. It can also be seen that as the leisure hours are

increasing the wage keeps on decreasing and the wage will be maximum when the

working hours are the maximum, that is 24.

Now the

next question is what happens if the individual is asked by his / her employer

to work for larger hours for some urgent work or for any other reason? In this

case for the larger number of working hours the leisure hours will be

decreasing since the working hours has been increased. In figure 4 the vertical

line that intersects the x- axis at 18 will shift towards left side to a

smaller value of 16 hours or 14 hours depending upon how many working hours

have been increased. The income will also increase and therefore the horizontal

line will shift upwards. In that case, both the new horizontal and new vertical

lines shown as red may not intersect with the indifference curve. This means

that to intersect the indifference curve the employer may have to increase the

hourly rate so that the curve can be intersected and same level of utility

index can be maintained for the individuals. In either case the total wage will

increase in both ways, firstly by working for more hours and secondly by

increased per hourly rate.