Answer
See below:
Work Step by Step
(a)
The system consists of models which describe demand and supply for low skilled labor.
The price at which demand and supply are equal is called equilibrium hourly wage. The quantity supplied and demanded at that price is called equilibrium number of workers.
The equilibrium hourly wage can be calculated as follows:
\[\begin{align}
& -0.325x+5.8=0.375x+3 \\
& 0.7x=2.8 \\
& x=4
\end{align}\]
This value is substituted in supply model or demand model to find the equilibrium number of workers.
\[\begin{align}
& p=0.375x+3 \\
& =0.375\left( 4 \right)+3 \\
& =1.5+3 \\
& =4.5
\end{align}\]
Hence, the equilibrium number of workers is \[4\text{ millions}\],and the equilibrium hourly wage is\[\$4.5\].
(b)
The price at which supply and demand is equal is called equilibrium price.
Substitute the price in demand and supply model to calculate the low skilled workers in demand and supplied.
(c)
The number of workers hired when the federal minimum wage was set at \[\$5.15\] is calculated by using this value in demand model.
\[\begin{align}
& p=-0.325x+5.8 \\
& 5.15=-0.325x+5.8 \\
& 0.65=0.325x \\
& x=2
\end{align}\]
Hence, number of workers employers will hire is\[2\text{ million}\].
(d)
The number of workers that would be available when the federal minimum wage was set at \[\$5.15\] is calculated by using this value in supply model.
\[\begin{align}
& p=0.375x+3 \\
& 5.15=0.375x+3 \\
& 2.15=0.375x \\
& x=5.7
\end{align}\]
Hence, the number of available workers is\[5.7\text{ million}\].
(e)
The number of more workers that are looking for work than employers are willing to hire when the federal minimum wage was set at \[\$5.15\] is calculated by subtracting the number of workers a calculated through demand and supply model.
That is,
\[5.7-2=3.7\text{ million}\]
Hence, the difference of number of available workers and workers employers is\[3.7\text{ million}\].
