A two-sector economy

Consider a two-sector economy with homogeneous labour and jobs in both sectors. Two
million workers supply their labour perfectly inelastically. Labor demand in both sectors can
be written as:
E1 = 1,800,000 – 100,000W1 and E2 = 1,800,000 – 100,000W2,
where E is employment and W is the wage.
(a) If both sectors are competitive, what is the market-clearly 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)?
(c) How many workers will be employed in sector 2, and what wage will they receive?
(d) What is the absolute union-wage gap?
(e) What is the relative union-wage gap?