Consider a two-sector economy with homogeneous labor and jobs in both sectors. Two million workers supply their labor perfectly inelastically. Labor demand in both sectors can be written as:

E₁ = 1,800,000 − 100,000 w₁ and E₂ = 1,800,000 − 100,000 w₂.

(a) If both sectors are competitive, what is the market-clearing wage, and how many workers are employed in both sectors?

(b) Suppose a labor union forms in sector 1. The union negotiates a wage of \($12\) per hour, and firms choose how much labor to employ. Anyone not employed in sector 1 is relegated to sector 2. How many workers will be employed in sector 1 (unionized)? How many workers will be employed in Sector 2, and what wage will they receive?

(c) What is the union-wage gap in part (b)? What would the union wage effect be if one controlled for the spillover effect?