Economics: I'm stuck with this wage differential question. If you wouldn't mind explaining or showing steps I would appreciate it. Thanks!

Let Aw E (wb Lug) denote the wage differential between industries a and b. Suppose that the wage offered by industry a is constant at wa = $8, but that b's wage, wb, is variable. Assume that the supply of labor to industry b is S(Aw) = 10 + 3 - Aw and that b's demand for labor is Daub) = 30 wb. What is the equilibrium compensating wage differential Aw*? Calculate and enter it below. Continuing with the previous question, now suppose that the (constant) wage offered by industry a is wa = $20. What is the equilibrium compensating wage differential Aw* now? Calculate and enter it below. Worked Problem 7.3 Compensating Wage Differentials Problem. The ice cream industry, a, offers the con- D (w / ) = 124 - 4. ( w / - w + w. ) = stant wage w = $6K, and the sewage industry the 124 - 4 . W - 4 . Aw variable wage, w. Assume the supply of labor to b is S(Aw) = 6 . Aw, where Aw = (w - w ), and b's Using w = $6K yields D(Aw) = 100 -4 . Aw. demand for labor is D(w) = 124-4 . wb. In equilibrium, the compensating wage differential What is the equilibrium compensating wage dif- adjusts to ensure supply equals demand in industry ferential Aw*? b: 6Aw = s = D = 100 - 4Aw. Hence 10Aw* = 100, Solution. Since our goal is to determine the equilib which implies the compensating wage differential rium compensating wage differential, Aw*, it is help- is Aw* = $10K. Therefore, those in the ice cream ful to first rewrite industry b's labor-demand curve industry are predicted to earn $6K and those in the as follows: sewage industry $16K