If the government imposes a subsidy on labor employed in the manufacturing sector, this reduces the effective wage rate which manufacturers have to pay to their employees.
Now, at equilibrium,
w = VMPL
If w falls, then this condition will be violated.
VMPL will become more than the wage rate, thus implying that the last unit of labor is contributing more in the production process than what the employer has to pay for him. As such, it becomes profitable to employ more units of labor. Hence, demand for labor in the manufacturing sector will increase.
Supply remaining unchanged, employment in the manufacturing sector should rise.
Now if there are unemployed workers in the economy, then this increase in demand for workers in the manufacturing sector will be satisfied from the pool of unemployed workers. In that case, the agricultural sector will remain totally unaffected. Wage and employment there would remain unchanged.
Thus, total employment should increase, given the increase in employment in the manufacturing sector and no change in employment in the agricultural sector.
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