Market Equilibrium with Work-Related Health Hazards

LABOR MARKET EQUILIBRIUM WITH WORK-RELATED HEALTH HAZARDS 

Economists refer to the equilibrium relationship between wages and injury risk as a hedonic wage function. Wages reflect not only the overall conditions in the labor market but also the relative attractiveness 

The problem confronting a worker is to find the level of injury risk (n) that maximizes expected utility. Given our initial assumptions we can mathematically represent expected utility as 

W(n) = the market wage function, observable to workers and firms, with W 0, 

Notice that expected utility is a weighted average of the utility if uninjured and the utility if injured with the weights equaling the probabilities of being (un)injured. Also notice the expected utility function explicitly considers both monetary and nonmonetary losses from 

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The differentials in the equation for hedonic labor market equilibrium, daldn and d ildn, describe how firms and workers match at the various degrees of exposure to work-related health hazards. There are three first-order conditions for the firm s maximum profit. We totally differentiated the three necessary conditions for maximum profit in (5.2)-(5.4) with respect to p and n to solve for the equilibrium pairings of firms and workplace safety levels, d x dn. Next, we re-arranged equation (5.5), the necessary condition for labor market equilibrium, to solve for da/dn, how workers sort against levels of injury risk. The differential equations of interest have the general expressions... 

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