10.1. Union wage premia and efficiency wages. (Summers, 1988.) Consider the efficiency-wage model analyzed in equations (10.12)-(10.19). Suppose, how- ever, that fraction f of workers belong to unions that are able to obtain a wage that exceeds the nonunion wage by proportion . Thus, w = M. (1+)wn. where w and w, denote wages in the union and nonunion sectors; and the average wage, wa, is given by fwu + (1f)wn. Nonunion employers continue to set their wages freely; thus (by the same reasoning used to derive [10.15] in the text), wn = (1 - bu)wa/(1 - ).

(a) Find the equilibrium unemployment rate in terms of ,

b. f, and .

(b) Suppose f = 0.15. - 1? (i) What is the equilibrium unemployment rate if = 0.06 and b By what proportion is the cost of effective labor higher in the union. sector than in the nonunion sector? (ii) Repeat part (1) for the case of = 0.03 and b = 0.5.