this is on modern labor economics ronald g ehenberg chapter

this is on modern labor economics ronald g ehenberg, chapter 8 number 6. please kindly ansewer my question. because there is not yet answer on the book solution. thank you

6. The demand for labor in Occupation A is LD-20-W, where LD = number of work- ers demanded for that occupation, in thousands. The supply of labor for Occu- pation A is LA 1.25+.5W. For Occupa- tion B, the demand for labor is similar, but the supply of labor is L.6W which is indicative of a more pleasant environment associated with that occupa- tion in comparison with Occupation A. What is the compensating wage differen- tial between the two occupations?

Solution

Occupation A

Ld = 20-W
La = -1.25+0.5W

Equilibrium wage = L_D=L_S

20-W=-1.25+0.5W
20 = 1.5W-1.25
1.5W= 20+1.25 = 21.25
W = 21.25/1.5 = 14.17

Occupation B

20-W=-0.5+0.6W
20 = 1.6W-0.5
1.6W= 20+0.5 = 20.5
W = 20.5/1.6 = 12.81

Looking at the wages,

wage differential = wage of Occupation A - wage of Occupation B

= 14.17-12.81 = 1.36

So, occupation B needs to pay 1.36 more in order to compensate labors of occupation A