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Hedonic Wage Function

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Up to this point we have seen a model with only two types of jobs:Prob of injury = 0 jobs and prob of injury = 1 jobs. (the indifference curves in the excel file, by the way, show more probs, but there we just look above 0 and 1). In the new model we will have jobs running with prob of injury from 0 to 1 and all in between. Plus we will have people with different types of utility functions.On the next slide I have an indifference curve for two different people. Indifference curves can cross for two different people. In fact lets focus first on the point where the curves cross. (Also note I am not saying the two people have the same utility, but on their own curve the utility stays the same.) Where the curves cross we know the prob of injury and the wage are the same. Now, move to a job with a higher prob of injury. The person with the steep indifference curve needs to get a higher wage to accept the riskier job, relative to the other worker. Both types of workers do not like risk, but the steep curve folks really do not like the chance of getting injured and thus need larger wage increases to take the riskier jobs compared to folks with flat indifference curves. Note here that when we look to just a little more on the prob of injury, the wage difference is the compensating differential for the individual.

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Prob of injury

Wage

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Indifference curves are related to how workers deal with probability of injury and wages. As you can imagine, workers have to get together with firms. Before we bring firms and workers together, let’s look at how firms deal with prob of injury and wages. I have an example on the next slide.Each curve on the next slide is called an isoprofit curve. Each curve has different combinations of prob of injury and wage the firm can offer and the firm would have the same level of profit. Notes:1) The isoprofit curves slope upward because reducing the probability of injury costs money. The only way the firm can pay higher wages then, and keep the same profit, is give up safety devices and thus live with greater prob of injury.2) The isoprofit curves farther northwest (or left) have lower profit because if you consider a given probability of injury (and thus a given expenditure on safety) then higher wages would reduce the profit.3) The isoprofit curves are said to be concave. To think about this start at the top of one of the isoprofit curves and then imagine reducing the prob of injury by increments of .001. The thinking is that there are diminishing returns to better safety. The first safety feature to incorporate should be the cheapest one. But then more safety becomes increasingly costly and thus to have the same profit the wages must be lowered accordingly. Then, the more returns to safety diminish, the more the wage the firm offers falls off.

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Prob of injury

Wage

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As an analogy, think about the safety of driving cars. On a road where people want to drive in both directions, probably the easiest way (and cheapest) to increase safety is to have people drive in the right lane in the direction they are going. The next thing to do is have a speed limit. But for many this is more costly because they want to get there quicker.Now, not all firms have the ability to make the workplace safer at the same costs. This means that isoprofit curves will be steeper or flatter for some firms. In fact, steep curves here means that it is very expensive to make the workplace safer, relative to flat curves because to get more safety wages are really sacrificed suggesting the safety features were expensive.Now, we will assume firms are in a competitive environment and have profits driven to zero in the long run. Thus when we consider firms and workers getting together we will only consider isoprofit lines that have zero profit. The logic is that if firms have profit other firms will enter in hopes of getting some of that profit that exists at other firms. Plus, firms with loses would eventually get out and do other things.

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Prob of injury

Wage

U1

U2

U3

Here I have one worker and three types of firms. The worker looks to maximize utility and thus will end up at U3. Here we note the indifference curves are flat meaning safety is not that big a deal to this worker and the worker ends up in a firm that has the hardest time making the work safe.

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Prob of injury

Wage

U1

U2U3

Here I have one worker and three types of firms. The worker looks to maximize utility and thus will end up at U3. Here we note the indifference curves are steep meaning safety is a big a deal to this worker and the worker ends up in a firm that has the easiest time making the work safe.

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Prob of injury

Wage

U3

Prob of injury

Wage

U3

Here I combined the last two graph and the two workers are different – I show U3 for each.

So, here, different workers end up at different firms.

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Prob of injury

Wage

U3

Prob of injury

Wage

U3

Here I reproduce the last graph, but add a line. The two workers I had before are at points A and B. More workers would show up along the line I have added. The solid line is called the hedonic wage function and it shows wages and probabilities of injury under which workers actually work.

A

B

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Now, I have been writing about indifference curves and isoprofit lines and these are hard to see in the real world. But, a result of this theory is the hedonic wage function and in the real world we should be able to collect data and plot out the function. What we note about the theory is that when jobs have a higher probability of injury the wages are higher in those jobs.

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Company prob of fatal injury annual earnings x Px Wx y Py = Px +.001 Wy = Wx + 7600.What I have in this table is a summary of information. From statistical work it has been found that when jobs have a .001 higher probability of a fatal injury the jobs will have $7600 more in annual income. The annual compensating wage differential is $7600.When we combine this table with our theory we say workers would take the riskier job if given $7600 more a year.Now the fatal injuries in company X per 1000 workers will be Px(1000) and in company y will be Py(1000) = Px(1000) + .001(1000). So one more worker is expected to die in company y than in company x. And, the 1000 workers each get $7600 more for a total of $7600000 in wages.With company y having one more worker expected to die and $7600000 in additional wages (per 1000 workers), we say the value of life is $7.6mil here.

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OSHA – Occupational Safety and Health Administration.OSHA is a federal program started in 1970 design to help workers be safe. One task of OSHA is to put a ceiling on the injury rate. In other words, they make companies be safe.We have just been through a theory where workers and firms get together and decide on how much safety and wages to have and now we have a government agency step in and mandate a certain amount of safety.You would expect the government to mandate injury rates lower than currently happening, or otherwise the program is useless and why have the government spend tax payer dollars on useless programs?Let’s look at the next slide to see one interpretation of this mandate. Firms and workers decide on P* and W*. The government then comes in and mandates Pbar (You see a P with a dash over it, read P bar), less than what firms and workers decide on.Now, the hedonic wage function suggests the wage will fall to Wbar because the experience in the data is that with prob of injury pbar the wage is wbar (the wage will probably be lower because the firms at P* has a harder time reducing risk – but…)

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Prob of injury

Wage

Prob of injury

WageWorkers will get lower wage.Workers will be on a lower indifference curve than the one shown and thus have less utility.Because they have to provide more safety the firms will have less profit.

W*

P*P

W

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Workers get lower wage, lower utility, lower prob of injury rates that they accepted with higher wages and firms get lower profit with the OSHA ceiling. Doesn’t seem like OSHA is good for the players. Again, this is one interpretation. The other interpretation is that workers do not know as much as firms about the level of probability of injury. In this case maybe OSHA can makes things better for some. Let’s turn to this in a graph on the next slide.Say firms are able to convince workers the probability of injury is Po when in fact it is P*. Now, the firm pays W* and the worker thinks their utility is really high with prob Po (I do not show the indifference curve here but it would be on a higher one.) In fact the worker has low utility because with the high prob of injury they actually get, even with the higher wage, they would prefer a lower wage and a lower prob of injury. If OSHA says a prob of injury pbar can result the worker would be happier even with the lower wage wbar.So, if the firm is deceitful it can have higher profit – this is very, very bad.

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Prob of injury

Wage

Prob of injury

WageWorkers will get lower wage.Workers will be on a higher indifference curve than in the case when they are tricked.Because they have to provide more safety the firms will have less profit, but they should because they were deceitful to begin with.

W*

P*Po

W

P

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Hedonic Theory - a more substantial theory

Disamenity - a negative in a job like risk of injury or unpleasant working conditions.

In the model developed it is assumed that all jobs are the same except for some disamenity, here assumed to be risk of injury.

Firms

Firms want to maximize profit. Risk of injury can be reduced, but it is costly. For firms to have the same level of profit, if risk of injury is reduced, wages must also be reduced to keep costs and profit the same.

In general, there are diminishing returns to risk of injury reduction. The same effort and cost reduces less risk the more risk already reduced. In other words, the cost of reducing equal increments of risk of injury increases - increasing marginal cost.

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Some firms are better than others at reducing risk of injury. In other words, some firms can reduce risk of injury by increasing cost less than other firms.

Workers

de gustibus non est disputandum - there is no accounting for taste, or something like that.

Hint: as we think about this don’t even think the person has the job yet.

Some workers tolerate risk of injury more than others. In other words, some works do not need as large a wage increase as other workers to accept the same increase in risk of injury. Stated another way, if risk is reduced, some workers will accept more of a reduction in wage than other workers.

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Risk averse folks are willing to give up a relatively large amount in wages to reduce risk of injury.

Conclusions

Workers with strong preferences for safe work (risk averse folks) will work for firms who can reduce risk of injury least expensively, although at a lower wage.

Thus, in competitive markets differences in wages will result due to differences in tastes of workers, and firms’ ability to deal with, risk of injury.

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Amenity - a positive in a job such as fringe benefits.

Back in 1929, 1.4% of total compensation was in the form of fringe benefits. In 1997 the % rose to 27.49.

Workers

All workers do not have the same preferences for fringe benefits. In general, we would expect that workers are willing to give up some wages for more fringe benefits. But some are willing to give up a relatively large amount in wages for the same increase in fringe benefits.

Firms

Firms look at the total compensation of employees as they consider costs and profit. Some firms can offer fringes at a lower cost than others - say buying power due to size.

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Firms may also offer certain types of fringes - like maternity leave - in the hopes of attracting certain types of workers.

Conclusion

Workers who have a relative preference for fringe benefits will work for firms who can provide them cheaper, although at lower wages.

At this time, empirical studies suggests this model is wrong. That is, wages and fringes have tended to go up together. The saving grace for the theory is that a third variable may not have been controlled for. As productivity has increased, all types of compensation has increased. So, by controlling for productivity gains, maybe the theory is still correct, wages and fringes move in opposite directions.