A country’s labor market is characterized by labor demand and labor supply given

Question

A country’s labor market is characterized by labor demand and labor supply
given by the following equations:
LD = 100 - 5W
LS = 10W - 20
where LD and LS are the quantity of labor demanded and supplied respectively,
in millions of workers, and W is the hourly wage rate.
(a) Suppose the labor market adjusts to competitive equilibrium. What is total
employment (L) and the competitive wage (W)?
(b) Suppose instead that there is a minimum wage of W = 9. What then is the
quantity of labor supplied (LS), the number of unemployed workers (U),
and the unemployment rate (u)?

Explanation / Answer

a) For competitive equilibrium

LD = LS

100 - 5W = 10W - 20

W = 8

Total employment = LD =LS = 100 -5x8 = 60

b) W =9

LD = 100 -5x9 = 55

LS = 10x9 - 20 = 70

=> The number of unemployed workers (U) = 70-55 = 15

the unemployment rate (u) = number of unemployed workers(U)/ total workers (LS)

= 15 / 90

= 0.1667

or 16.67 %

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