Question

1. Union A finds that a wage of $4 per hour leads to demand for 20,000 person hours and a wage of $5 per hour leads to demand for 10,000 person hours. Union B finds that a wage of $6 per hour leads to demand for 30,000 person hours, while a wage of $5 per hour leads to demand for 33,000 person hours.
   1. Which union faces the more elastic demand curve? Describe 2 Hicks-Marshall laws that might explain that union’s elasticity
   2. Which union will be more successful in increasing the total income (wages times person hours) of its membership?

Answer 1

Let wages be denoted by w and labour demand be denoted by L.

(a) Union A:

Elasticity of labour demand = % change in lobour demand / % change in wages

e = (W/L) * (ΔL/ΔW)

Here, W = $4, L = 20,000

ΔW = 5 - 4 = $1

ΔL = 10000 - 20000 = -10,000

Thus,

e_A = (4/20000) * (-10000/1) = -2

Union B:

Elasticity of labour demand = % change in lobour demand / % change in wages

e = (W/L) * (ΔL/ΔW)

Here, W = $6, L = 30,000

ΔW = 5 - 6 = -$1

ΔL = 33000 - 30000 = 3000

Thus,

e_B = (6/30000) * (3000/-1) = -0.6

Since e_A > e_B , union A faces more elastic demand curve.

Hicks-Marshall laws:

1. The own-wage elasticity of demand for labour is high when the price elasticity of demand for the product being produced is high, all other things being equal.

2. The own-wage elasticity of demand for labour is high when the other factors of production can be easily substituted for labour, other things being equal.

(b) When elasticity of labour demand in elastic i.e. e > 1, total income will decrease as a result of increase in wages and vice-versa. When e < 1 i.e. inelastic, total income will increase with increase in wages and vice-versa.

Since e_B < 1, demand for labour is inelastic, which means that union B will be more successful in increasing the total income of its membership.