Question

1. The market demand for labour is given by w = 18 – 0.05L, where w is the wage rate ($/week) and L is the number of workers the firm want to employ. The market supply of labour is given by w = 10 + 0.05L, where w is the wage rate ($/hr) and L is the number of workers who want to work.

a. What is the equilibrium wage rate?

b. If the government introduces the minimum wage rate of $14.75/hr, what would be the unemployment rate?

Answer 1

Answer

1. (a) Equilibrium wage rate is $19/hr.

The market demand for labor is;

w = 18 – 0.05L.....(1)

The market supply of labor;

w = 10 + 0.05L......(2)

At the equilibrium level, the demand for labor is equal to the supply of labor.

  18 – 0.05L = 10 + 0.05L

Or, – 0.05L - 0.05L = 10 - 18

Or, - 0.1L = - 18

Or, L = - 18 / -0.1

Or, L = 18 / 0.1

Or, L = 180

So, equilibrium quantity of labor is 180.

Now, putting the value of L in equation(1), we get,

w = 10 + 0.05 * 180

Or, w = 10 + 9

Or, w = 19

So, equilibrium wage rate is $19/hr.

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1.(b) unemployment rate = 16.7%

If, government introduces minimum wage rate of $14.75/hr, then the labor demand , and labor supply would be as follows;

From equation(1), we get the market demand for labor is;

w = 18 – 0.05L

Now, putting the value of minimum wage rate in place of 'w', we get,

14.75 = 18 – 0.05L

Or,  0.05L = 18 - 14.75

Or, 0.05L = 3.25

Or, L = 3.25 / 0.05

Or, L = 65

So, at minimum wage rate of $14.75/hr, the labor demand is 65.

From equation(2) , we get the market supply of labor is;

w = 10 + 0.05L

Now, putting the value of minimum wage rate in place of 'w', we get,

14.75 = 10 + 0.05L

Or, - 0.05L = 10 - 14.75

Or, - 0.05L = - 4.75

Or, L = - 4.75 / - 0.05

Or, L = 95

So, at minimum wage rate of $14.75/hr, the labor supply is 95.

Thus, at minimum wage rate of $14.75/hr, the labor supply is greater than labor demand by the amount, 95 -65 = 30.

So, the number of unemployment is 30.

From '1.(a)', we see that at the equilibrium level, the total quantity of labor in the market is 180.

Unemployment rate = (30 /180) * 100

Or, unemployment rate = (1/ 6) * 100

Or, unemployment rate = 16.7 (approx.)

The unemployment rate is 16.7%.

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