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Fixed costs of working and the decision to work 1


1. Fixed Monetary Costs of Working
2. Fixed Time Costs of Working
3. Estimation of Fixed Costs of Working for an Individual

In my essay I would like to consider an important component of analysis of theory of decision to work. It is the fixed costs of working. In other words, the costs that incurred for any worker and thus, cannot be avoided once a person decided to take a work place. Such costs include commuting, child care, dinners at the work place etc. These costs are treated as being fixed, in the sense that they will be assumed not to vary with the number of hours an individ¬ual actually works.
These fixed costs of working typically include both monetary and time components. I will analyze both of them. Then I will approximately estimate these fixed costs for a typical employee and consider the results.

1. Fixed Monetary Costs of Working
Fixed monetary costs of working are those that have monetary outlay. The examples are price of lunch at the work, salary for the baby-sitter, petrol price etc.

Fig.1 Work/Leisure Choice with Fixed Money Costs of Working

Fig.1 shows several indifference curves for an individual who has non-labor income in the amount aT. If this individual chooses not to work at all, he or she will locate at point a and have a utility level of U1. If the individual does choose to work, a fixed per-period cost of ab is incurred. Hence, if the individual works, the budget line starts from point b, not from a.
The absolute value of the slope of the budget line represents the wage rate. Rotating hypothetical budget lines around point b, we eventually reach tangency (at point C) with the indifference curve that represents the individual's utility level, U1, if he or she doesn't work at all. At point С the individual is receiving a wage equal to the absolute value of the slope of budget line bd, is working Т — L2 hours, and is just indifferent to not working. Any decrease in this wage will cause the individual to drop out of the labor force, because utility level U1, will no longer be attainable if he or she works any hours. The wage represented by the slope of bd is called the person's reservation wage, that is the lowest wage for which he or she will work. [1]
From Fig.1 we see that if the fixed costs were to increase to ae, we will derive a new budget line tangent to U1 – ef. It has a sleeper slope than bd; an increase in the fixed costs of work will tend to raise the reservation wage of potential workers. It can also be noted that the tangency point of budget line ef with indifference curve U1 is at point B, which because it lies to the left of point С implies that those who work will consume fewer leisure hours than was the case with fixed costs of ab.
Now suppose work¬ers facing fixed working costs of ab could earn the wage implied by budget line bg in Fig.1. These workers would locate at point A and could thereby achieve utility level U2. Since points on curve U2 are superior to points on curve U1, they clearly prefer working to being out of the labor force.
However, if the fixed costs of work were to increase from ab to ae, and wages were to remain constant, the relevant budget line for these workers becomes ef. Now they can achieve only utility level U1, the same utility they can get by not working. If they continue to work they will desire to work mere hour. These workers, however, may decide not to work and to drop out of the labor force, because the rise in the fixed monetary costs of work has increased their reservation wage to the point at which it equals their actual wage.
Increasing fixed costs of work, then, will tend to increase the hours of work for some workers but cause others to drop out of the labor force. Conversely, decreasing fixed costs would decrease hours of work for some workers but induce others to enter the labor force. [2]

2. Fixed Time Costs of Working
Fixed time costs of working are those associated with time outlay. The examples can be commuting or transporting children to kindergarten.

Hours of Leisure

Fig.2 Work/Leisure Choice with Fixed Time Costs of Working

Let us consider Fig.2. There, again, an individual has non-labour income in the amount аT and, if this individual does not work, will have a utility level of U1. Now suppose that if the individual does work, he or she incurs fixed time costs in the amount ab. In this case, the maximum number of hours a day available for work or leisure is no longer Т but rather T1. The individual's budget line starts at point b if he or she works, and its slope is minus the wage rate. If this budget line is bc the individual will locate at point A and work T1 — L1 hours.
If the individual's wage rate were lower, the budget line would rotate around point b and become flatter than the slope of bc. If the budget line were bh, the individual could maximize utility by locating at point D and by working T1 - L2 hours. At this point, however, the individual's utility is equal to U1, the utility level he or she would attain from not working, so he or she would be indifferent between working and not working. Any lower wage would clearly induce the indi¬vidual to drop out of the labor force.
Suppose now that the fixed time costs of work increase from ab to ad. A worker originally facing budget line be now faces budget line de, will locate at point B, and will work T2 ~ L3 hours while consuming L3, hours of leisure. As long as leisure and in¬come are both assumed to be normal goods, hours of both work and leisure time will be reduced by the increase in time costs of work. Further increases in the time cost of work leads to further reduction in hours of work. [3]
This model suggests that anything that decreases the time costs of work will lead to increases in hours of work, ceteris paribus. [4]

3. Estimation of Fixed Costs of Working for an Individual Worker
Now let us consider the fixed costs that can be incurred by a typical employee.
All monetary costs can be divided into four parts: - transportation, - clothing, - food at work, - child care (let us assume our considered employee has one child of preschool age). The estimation of fixed costs per month can be the following:

Type of Cost
Money Paid (RUR)

- Commuting
600 (monthly metro ticket) – 3 000 (operating a car)

- Clothing
2 000

- Food
3 300

- Child Care

1000 (the cheapest kindergarten) – 14 000 (average salary of a baby-sitter)

Total 14 600

It is a very approximate estimation because the limits, that is the lowest and the highest possible amounts of money paid for these types of costs cannot be calculated exactly. For example, a person can bring home food to the workplace and thus not pay anything for the dinner at work. Also clothes, services of the nanny etc. can vary greatly. For convenience, I decided not to take extreme variants.
Now, if we look at the Fig.1, we can say that in our case, fixed money costs ab equal 14 600 RUR. So now this person should have the wage rate not less than the slope of bd curve to obtain utility not lower than in the case he does not work at all. If his wage rate increases to bg, he will reach the higher level of utility U2. But if after that increase in wage someday his fixed costs become more than 14 600 (for example, they increase to ae), he will become indifferent between working for this salary and not working at all.
Now we shall estimate fixed time costs of earning per day for a typical employee:

Type of Time Cost Time (hours)
Commuting 1.5 hour
Taking children to and from kindergarten 1 hour
Total 2.5 hours

Now, considering Fig.2, we can see fixed time cost for our typical employee equals 2.5 hours=ab. And he is indifferent between working for salary equals minus slope of bh (in this case he will have only T1=21.5 hours for work and leisure) or not working at all (he will have T=24 hours for leisure). If wage rate is lower than bh, he will drop out the labour force. But if the wage rate increases to bc slope, he will be able to gain higher utility level U3.

I have analyzed the nature of fixed costs and the effects they have on individual`s decision to work. I have considered what influence both monetary and time fixed costs have in different situations and at different levels of wage rates. I have seen that the notion of reservation wage and considering employee`s set of indifference curves are very important in decision-making whether to work or not.
Then I calculated the fixed costs for a typical employee and tried to make some conclusions basing on the study of the theory of fixed costs.

Endnotes Section:

[1] Ehrenberg R. G., Smith R.S. “Modern labor economics: Theory & Public Policy”; Addison Wesley Higher Education, 2000
[2] “Fixed Costs and Labor Supply” John F. Cogan ; June, 1980
[3] Ehrenberg R. G., Smith R.S. “Modern labor economics: Theory & Public Policy”; Addison Wesley Higher Education, 2000
[4] “Fixed Costs and Labor Supply” John F. Cogan ; June, 1980

1) "Labour Economics" Steven Smith, 2003
2) en.wikipedia.org/wiki/Labour_economics
3) “Fixed Costs and Labor Supply” John F. Cogan ; June, 1980
4) http://www.moscowfaq.ru/all_question/experience/2008/February/4156/105
5) Ehrenberg R. G., Smith R.S. “Modern labor economics: Theory & Public Policy”; Addison Wesley Higher Education, 2000

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