Question

Suppose all workers in an economy have the same preferences represented by U = w √ n where w is the wage and n is the degree of noise that is associated with the job they do. There are only three types of jobs in the economy, a job with little noise (n = 1/9), some noise (n = 1/4), and lots of noise (n = 1). If the job with little noise offers a daily wage of $100 and the economy is in the equilibrium (thus, no one has an incentive to change jobs), what would the wage be for jobs with some noise and jobs with lots of noise? What is the compensating wage differential between the job with little noise and the job with lots of noise?

Answer 1

The additional income that must be given to a person in order to accept an unpleasant or undesirable working condition is called as compensating wage differential

Given, the utility finction, U = w* sqrt(n)

sqrt (n) = square root of n

The wage of the job with little noise is given as $100.

The utility of the job with little noise is equal to

U = 100* (1\9)^1\2

= 100 * 1\ 3

=33.33

Now, the wage of job with some noise and lot of noise is calculated by substituting the utiluty in the given function with different values of n.

In the case of job with some noise

U = W * n^1\2

33.33 = W * (1\4)^1\2

33.33 = W * 1\2

W = 66.66

In the case of job with lot of noise , n= 1

33.33 = W * 1

W = 33.33

Now, the wage differentials between the jobs with little noise and lots of noise is the difference between their wages

Wage differential = 100_ 33.33 = 66.67