Question

In the country of Macroland, the labor market is represented by the following equations:

                        Q_D = 600 – 40W

                        Q_S = -50 + 60W

where Q is the quantity of Labor in millions of workers and W is the wage rate.

(a) Currently, the minimum wage Law in Macroland is $10 per hour. Calculate, the number of labor supplied, the number of labor demanded, the number of unemployed and the unemployment rate.            

(b) If Macroland eliminates the minimum wage law, what would happen to total employment, wage rate and the unemployment rate? 0

(c) In a clearly labeled graph, show your results for (a) and (b).

Answer 1

Answer

(a) Number of labor supplied = 500; Number of labor demanded = 200; Number of unemployed = 300; Unemployment rate = 70%.

The labor demand function in Macroland is as follows;

Q_D = 600 – 40W..........(1)

The labor supply function in Macroland is as follows;

Q_S = -50 + 60W..........(2)

Currently, the minimum wage Law in Macroland is $10 per hour.

At wage rate $10 per hour, the demand for labor in Macroland will be,

Q_D = 600 – 40 * 10

Or,  Q_D = 600 – 400

Or,  Q_D = 200

At wage rate $10 per hour, the supply of labor in Macroland will be,

Q_S = -50 + 60 * 10

Or, Q_S = -50 + 600

Or, Q_S = 550

The number of unemployed = Qs - Qd = 550 - 200 = 350

Unemployment rate = (Number of unemployed / Total labor force) * 100

Or,  Unemployment rate = (350 / 500) * 100 = 70%

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(b) Total employment = 340; Wage rate = $6.5; Unemployment rate = 0%

If Macroland eliminates the minimum wage law, then in the free market, the market equilibrium will happen, when QD = QS

  600 – 40W = -50 + 60W

Or, – 40W - 60W = - 50 - 600

Or, - 100W = - 650

Or, W = 6.5

The equilibrium wage rate is $6.5.

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

Q_D = 600 – 40 * (6.5)

Or,   Q_D = 600 – 260

Or,   Q_D = 340

Again, putting the value of 'W' in equation(2), we get,

Q_S = - 50 + 60 * (6.5)

Or, Q_S = - 50 + 390

Or, Q_S = 340

Q_D = Q_S = 340

So, the total employment is 340.

Unemployment rate = (0 / 340) * 100 = 0%

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(c)

Wage($)	Labor Demand (600 – 40W)	Labor Supply ( -50 + 60W)
0	600	-50
5	400	250
6.5	340	340
10	200	550
15	0	850

In the above figure, we see that at $10 wage rate, there is excess supply(ES) of labor of 300 units.

At the wage rate of $6.5, both the labor demand and labor supply are 340 units. Here, point 'E' shows the equilibrium point in the market.

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