A no liability rule

Suppose, then, that direct negotiations over care are not possible. We will assume throughout the analysis that the level of care taken by firms is observable and can form part of an employment contract, but that the level of care taken by workers (which occurs subsequent to the contract being agreed to) is not.

First, suppose that a rule of no liability is in place, so that employees must bear the full costs of any accident. Note that for any level of care provided by firms under a no liability rule, workers will be induced to supply the level of care that minimises wvxv + H(xi,xv). The reason for this is straightforward: having chosen their level of care, firms will - in order to minimise their wage bill of o + wvxv + H (xt, xv) - offer the wage that makes these costs as small as possible. Workers are free to choose any level of care that they wish, but having observed the level of care and the wage that firms are offering, they will choose to supply the level that minimises o + wvxv + H (x{, xv), since this gives them the highest net benefit at the wage that has been offered to them. Any other level of care would leave them out of pocket, since under a no liability rule it is workers who bear the costs of any accident.

Will employers take any care under this legal rule? Suppose that they do not take any care. We will show that this cannot occur in a competitive equilibrium.

To see this, note that for any wage O, in this section in the absence of any care that is taken by employers, workers would need to be given a wage of at least:

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in order to be willing to supply labour, where x° minimises wvxv + H(0,xv). Since workers' cost of care is wvx0 and their expected harm is H (0, x0), they will not be willing to work unless (6.24) is satisfied.

So, suppose that firms take no care and pay this wage. Then all workers accept and the firm's profits are:

which we assume to be non-negative. Is this situation sustainable as an equilibrium? No. Suppose that a 'rogue' firm offered a lower wage of со* < oo° in exchange for a commitment to supply the efficient level of care, xi*, and where

This rogue firm's costs are:

and so it will make greater profits from undertaking this strategy as long as:

On the other hand, workers will be no worse off under this wage, since:

Is a wage-care combination that satisfies (6.25) and (6.26) possible? If it is, then the rogue firm will earn higher profits than all of its competitors and leave workers as well off as they were with the other firms. Now since (x*, x*) is efficient, we know that:

If the 'rogue' firm offers the worker the wage v*, it will leave workers no worse off, but the increase in profit to the 'rogue' firm will be:

Where the last inequality follows from (6.27). Therefore, a situation where firms supply no care cannot be an equilibrium.

But this reasoning applies to any positive level of care, with xt Ф x*, which means that the only competitive equilibrium under a no liability rule is where both firms and workers supply the efficient level of care. To check that this really is a competitive equilibrium, note that in such an equilibrium, firms will offer a wage of:

At this wage, workers will voluntarily choose to supply x* units of care, even though firms cannot monitor or observe the level of care taken by workers. And, beginning from this equilibrium, there is no combination of care and wages that a 'rogue' firm could offer that would increase profits and be accepted by workers. Hence it is the only competitive equilibrium.

 
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