Question

Consider an economy with two sectors: manufacturing and services. Demand for labor in manufacturing and services are described by these equations: L m = 320 − 8 Wm ,L s = 150 − 4 W s where L is labor (in number of workers), W is the wage (in dollars), and the subscripts denote the sectors. The economy has 248 workers who are willing and able to work in either sector. If a minimum wage of $25 is imposed in the economy and that each sector wants to maximize its employment, what is the unemployment rate (in percentage terms)?

Answer 1

Lm = 320 - 8Wm

put Wm = 25

=> Lm = 320 - 8(25)

=> Lm = 320 - 200

=> Lm = 120.

Manfacturing sector will demand 120 workers at a minimum wage.

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Ls = 150 - 4Ws

Put, Ws = 25

=> Ls = 150 - 4 (25)

=> Ls = 150 - 100

=> Ls = 50

Service sector will demand 50 workers at a minimum wage.

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Total employed worker = 120 + 50 = 170.

There are 248 workers who are willing to work and able to work in either market.

So, the labor force = 248.

Labor force = employed + unemployed

=> 248 = 170 + unemployed

=> Unemployed = 248 - 170 =78

There are 78 workers will remain unemployed .

Unemployment rate = (unemployed worker / labor force)*100

Unemployment rate = (78 / 248) * 100

Unemployment rate = 31.45%

Answer: Unemployment rate is 31.45%