Question

Graph the following labor market model:

S W = 4 + 2L

D W = 30 – 2L

What is the quantity of labor supplied and labor demanded at a wage of 10? Would there be a surplus or a shortage of labor ? would you expect this surplus or shortage to persist in competitive labor market?

Answer 1

Given, supply function of labour;

W = 4 + 2L
Ls = W/2 - 2

where W = wages
L = labour

Demand function of labour;

W = 30 - 2L
Ld = 15 -W/2

where W = wages
L = labour

At equilibrium level, demand of labour should be equal to quantity of labour;

Ls = Ld
W/2 - 2 = 15 - W/2
W/2 + W/2 = 15 + 2
W = 17

L = 17/2 - 2
L = 6.5

When, wage is; W = 10

Supply of labour will be;

10 = 4 + 2L
10 - 4 = 2L
6 = 2L
Ls = 3

Demand of labour will be;

10 = 30 - 2L
2L = 30 - 10
2L = 20
Ld = 10

As we can see, quantity of labour demanded is greater than the quantity of labour supplied;

Ld > Ls
10 > 3

Therefore, there will be excess demand in the market, which means there will be a shortage in the market.

A shortage in the labour market arises when quantity of labour demanded is greater than the quantity of labour supplied due to lower wages. But this shortage will not persist long in competetive labour market. In competetive labour market, equilibrium level of wages and labours are determined by the market forces of demand and supply. When wages are low, demand will be greater and supply will be lower for labours, but as many people will be unemployed after some time they will start to increase their supply, and thus the level of supply will tend to increase to fulfill the demand and wages and labour will reach upto equilibrium point.