Income and Substitution Effects: Difference between revisions

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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 ? denote other incomes or benefits.
Let A denote leisure hours.
The utility function and budget constraint can be expressed as following:
max U(w L + ?, A) such that L + A ? k.
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 curve labelled 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.
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In the labor economics model, labor is supplied by the workers, who are trying to maximize their utility by choosing between work and leisure. As rational thinkers, workers are assumed to be always making a decision of how many hours to work and how many hours to rest, while being constrained by the hours available to them in a day.
 
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 substitution, 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:
 
 
 
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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).
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The following diagram shows the trade-off between leisure time and time spend on income generating activities. The straight line is the 24 hour constraint, since there are a total of 24 hours in a day, and this is the maximum amount of hours workers can spend working or resting. The allocation decision is taken by looking at the time constraint and the indifference curve labeled IC, which 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 tangent to the constraint line shows how much time a person will spend working and resting. In the diagram that would be point A.
 
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 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 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 utility 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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<center>[[Image:Image1.png|thumb|Description]]</center>
==Income Effect==
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When wages increase, the income effect states that a worker feels wealthier and that he needs to work less to have the same income. The effect will result in the laborer placing a greater demand on goods, services, and non-market activities so that he/she will cut down on supply of labor.
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Continuing on the same line of thought, if the preference for consumption is measured by income rather than hours of work, the diagram can be redrawn as to show a variety of other effects. In that case, the slope of the budget constraint becomes the effective wage rate and point A, the utility maximizing point, now reflects the equality between the wage rate and the marginal rate of substitution of leisure for income, which is the first derivative of the indifference curve at that point, or its slope. Since that marginal rate of substitution is also the ratio of the marginal utility of leisure (MU<sup>L</sup>) to the marginal utility of income (MU<sup>Y</sup>), then:
==Substitution Effect==
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The substitution effect is simply  when the laborer feels that  because the wage has increased the worker realizes that by involving himself in non-market activities he is missing the opportunity to increase savings. Therefore, the result will be an increase in the supply of labor. For temporary wage increases the substitution effect dominates.
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<center>[[Image:Effects2.png|thumb|Description]]</center>
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If the real wage is increased, then the worker’s constraint line will pivot up from X,Y<sub>1</sub> to X,Y<sub>2</sub>, showing that he can now purchase more goods and services by doing the same amount of work. Consequently, the worker’s utility will increase from point A on IC<sub>1</sub> to point B on IC<sub>2</sub>. The shift from point A to point B can be explained in greater detail by looking at the income and substitution effects.
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<center>[[Image:Image3.png|thumb|Description]]</center>
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The shift in the diagram above can be shown in a slightly different and more detailed way by depicting both effects separately. In the diagram below, the pure income effect is shown as the movement from point A to point C. Consequently, consumption increases from Y<sub>A</sub> to Y<sub>C</sub> and leisure time increases from X<sub>A</sub> to X<sub>C</sub>.
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As the wage rate rises, the worker will also substitute work hours for leisure hours in order to profit from the higher wage rate, or substitute away from leisure because of its higher opportunity cost. That effect, the substitution effect, is represented by the shift from point C to point B.
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<center>[[Image:Image4.png|thumb|Description]]</center>
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The shift from point A to point B is the net result from both effects. The relative magnitude of the two effects depends on the circumstances. In some cases the substitution effect is greater than the income effect, whereas in other cases the income will be greater than the substitution effect.
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<center>[[Image:Image5.png|thumb|Description]]</center>
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Considering only the two effects, if the substitution effect dominates the income effect, the labor supply curve will slope up and to the right, as it does at point E in the diagram below. This worker will choose to continue increasing the labor he supplies with the increasing wage rate up until point F where he is working H<sub>F</sub> hours. At that point, the income effect starts dominating and the worker will start reducing the amount of labor hours supplied. Where the supply curve is sloping up and to the right the elasticity of labor supply is positive and where it is sloping up and to the left it is negative (at point G for example). At different levels of labor supplied and income received the direction of the slope can be different for all individuals. In the next sections we will discuss why that is so and what are the consequent ramifications for the different workers.
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[http://www.factbook.org/ Factbook.org]

Latest revision as of 23:24, 6 May 2006

Page Overview | Income and Substitution Effects | Female vs Male Behavior in the Labor Market | Opportunity Cost of Leisure Time | Works Used

In the labor economics model, labor is supplied by the workers, who are trying to maximize their utility by choosing between work and leisure. As rational thinkers, workers are assumed to be always making a decision of how many hours to work and how many hours to rest, while being constrained by the hours available to them in a day.

The following diagram shows the trade-off between leisure time and time spend on income generating activities. The straight line is the 24 hour constraint, since there are a total of 24 hours in a day, and this is the maximum amount of hours workers can spend working or resting. The allocation decision is taken by looking at the time constraint and the indifference curve labeled IC, which 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 tangent to the constraint line shows how much time a person will spend working and resting. In the diagram that would be point A.

File:Image1.png



Continuing on the same line of thought, if the preference for consumption is measured by income rather than hours of work, the diagram can be redrawn as to show a variety of other effects. In that case, the slope of the budget constraint becomes the effective wage rate and point A, the utility maximizing point, now reflects the equality between the wage rate and the marginal rate of substitution of leisure for income, which is the first derivative of the indifference curve at that point, or its slope. Since that marginal rate of substitution is also the ratio of the marginal utility of leisure (MUL) to the marginal utility of income (MUY), then:

File:Effects2.png



If the real wage is increased, then the worker’s constraint line will pivot up from X,Y1 to X,Y2, showing that he can now purchase more goods and services by doing the same amount of work. Consequently, the worker’s utility will increase from point A on IC1 to point B on IC2. The shift from point A to point B can be explained in greater detail by looking at the income and substitution effects.

File:Image3.png



The shift in the diagram above can be shown in a slightly different and more detailed way by depicting both effects separately. In the diagram below, the pure income effect is shown as the movement from point A to point C. Consequently, consumption increases from YA to YC and leisure time increases from XA to XC.

As the wage rate rises, the worker will also substitute work hours for leisure hours in order to profit from the higher wage rate, or substitute away from leisure because of its higher opportunity cost. That effect, the substitution effect, is represented by the shift from point C to point B.

File:Image4.png



The shift from point A to point B is the net result from both effects. The relative magnitude of the two effects depends on the circumstances. In some cases the substitution effect is greater than the income effect, whereas in other cases the income will be greater than the substitution effect.

File:Image5.png



Considering only the two effects, if the substitution effect dominates the income effect, the labor supply curve will slope up and to the right, as it does at point E in the diagram below. This worker will choose to continue increasing the labor he supplies with the increasing wage rate up until point F where he is working HF hours. At that point, the income effect starts dominating and the worker will start reducing the amount of labor hours supplied. Where the supply curve is sloping up and to the right the elasticity of labor supply is positive and where it is sloping up and to the left it is negative (at point G for example). At different levels of labor supplied and income received the direction of the slope can be different for all individuals. In the next sections we will discuss why that is so and what are the consequent ramifications for the different workers.

Factbook.org

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