# Quiz 5 : Compensating Wage Differentials

This particular claim supporting the green movement can be well understood by using the concept of compensating differential. From our basic understanding of compensating differential, it is understood that in a two-commodity framework - wage is considered a good commodity; furthermore, risk of job injury is considered a bad commodity. From that perspective any worker would like to work for risky jobs only if he is provided a wage rate that is higher than her reservation price, otherwise she/he would like to work for a safe job for a lower wage. From this it can be argued that since safety is costly and if firm invest in green technology and provide a safe work environment to the workers then worker will be working in lesser wages, and depending on the productivity differential it can be worked out whether it is becoming profitable for firm or not. Hence, the claim by environmentalist is partially correct and the holistic understanding is by focusing on wage differential and productivity.

If in a labor market there are only two types of jobs safe jobs and risky jobs then in that case an utility analysis can guide us a worker's decision about which job to chose and which not to. Here the assumption is that all the workers are risk averse and that is how risk of injury from a job becomes a 'bad' good. And worker would require more wage as compensation to take up a risky job over a safe job. Now let the utility function is- Here u= utility derived by the worker, w = wage rate they earn on the job, r = risk of injury on the job. Now a worker's choice can be depict in a stylized manner from the diagram below. Here in the above diagram in X axis p refers to probability of injury and in the Y axis w refers to wage rate. Suppose initially worker earns a wage of w0 with a corresponding utility level u0. The worker would prefer the safe job is she is offered wage rate of w1. But she would prefer the risky job over the safe job if she gets wage rate w3. And she is indifferent in the wage rate w2. Hence her reservation price is r which is equal to w2-w0. And if she gets anything more than r she will definitely go for a risky job and then she would prefer a risky job over a safe job. This is how a worker would choose between two jobs when only two types of jobs are available- safe and risky.

a) The necessary algebraic steps are as follows- Now we know that a profit-maximizing firm will offer a risky environment only if When = Then from here, we can get 5-6) i.e. Firm will offer a safe environment if Firm will offer a risky environment if …..(5-6). b) The supply curve in the below figure is upward sloping because with the increase in wage gap between safe job and risky job, more and more worker will like to go for risky jobs. Here refers to the value of productivity gain per additional worker if this exceeds the wage increases firm needs to provide in order to induce worker for risky a risky job otherwise it is profitable for the firm to go for safe job. c) In that case labor demand for this kinds of jobs will rise which can be depicted through the figure below. If earlier L1 worker were involved then due to the advancement in technology up to L2 mount of worker can be employed in risky jobs.

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