Question

Suppose the economy consists of a union and nonunion sector. The labor demand curve in each sector is given by L =1,000,000−20w. The total (economy wide) supply of labor is 1,000,000 (500K in each sector) and it does not depend upon the wage. All workers are equally skilled and equally suited for work in either sector.

(a) If a competitive labor market existed in each sector, how many would work in each sector? What would be the wage in each sector?

(b) Suppose now a monopoly union sets the wage at $30,000 in the union sector. What will be the wage in the nonunion sector? What is the union wage gap? What is the size of the deadweight loss resulting from the monopoly union?

Answer 1

a).

Consider the given problem here there are two sectors union and nonunion both of them having same demand for labor that is, L = 1,000,000 – 20*W, and the total supply of labor is 1,000,000. All the workers are equally equally skilled and suited for work in either sector. So, under the perfect competition both the sector will employ equal number of workers that is “500,000”.

So, the demand for labor can also be written as “W = 1,000,000/20 – L/20 = 50,000 – 500,000/20 = 25000. So, the equilibrium wage is “25000”.

b).

If a monopoly union set the wage at $30,000 in union sector then the employment is union sector is, L = 1,000,000 – 20*W = 1,000,000 – 20*30000 = 400,000. So, the employment is union sector decreases to 400,000. Now, under the perfectly competitive market the 600,000 worker will be employed in nonunion sector. So, the wage is.

=> W = 1,000,000/20 – L/20 = 50,000 – 600,000/20 = 20,000, => Wn2 = 20,000. Consider the following fig.

Here as the wage in union sector increase the employment decreases. So, it create dead weight loss by the area E1AB.

=> E1AB = 0.5*(Wu2-Wn2)*(L1-L2) = 0.5*(30,000-20,000)*(500,000-400,000).

=> E1AB = 0.5*10,000*100,000 = $500,000,000.