Suppose that the market labor supply and labor demand equations are given by Qs = 5W and Qd = 30 - 5W. The government has passed a law that subsidizes wages by $1 per hour. The equilibrium wage and quantity of labor with the subsidy is?
$4 and 15 workers respectively.
$2.5 and 12.5 workers respectively.
$3.5 and 17.5 workers respectively.
$3.5 and 10 workers respectively.
To solve, I rewrote the supply and demand equations as W=f(Q). So: Ws = Qs/5 and Wd = 6 - Q/5. (So far, this is just algebra)
Now then, the $1 per worker subsidy has the effect of lowering the supply equation by $1 for all levels.
So, Ws' = Qs/5 - 1. Now set supply = demand and solve for Q.
That is Q/5-1 = 6-Q/5
Take it from here
To find the equilibrium wage and quantity of labor with the subsidy, we need to determine the new labor supply and labor demand equations after the subsidy is implemented.
The labor supply equation with the subsidy can be found by subtracting the subsidized amount ($1) from the original labor supply equation:
Qs = 5W - $1
The labor demand equation remains the same:
Qd = 30 - 5W
To find the equilibrium wage and quantity of labor, we set the labor supply equal to the labor demand:
5W - $1 = 30 - 5W
Now, solve for W:
10W = 31
W = $3.1
Substitute this value of W back into either the labor supply or labor demand equation to find the quantity of labor:
Qs = 5($3.1) - $1
Qs = 15.5 - $1
Qs = 14.5
Therefore, the equilibrium wage and quantity of labor with the subsidy are $3.1 and 14.5 workers, respectively.
None of the provided options match the result calculated. It appears there may be an error in the given options.
To find the equilibrium wage and quantity of labor with the subsidy, we need to set the quantity supplied equal to the quantity demanded and solve for the wage.
Given:
Market labor supply: Qs = 5W
Market labor demand: Qd = 30 - 5W
With the subsidy, the wage will be decreased by $1 per hour. So, the new labor supply equation will be Qs = 5(W - 1).
Setting the quantity supplied equal to the quantity demanded:
5(W - 1) = 30 - 5W
Now, solve for W:
5W - 5 = 30 - 5W
10W = 35
W = 35/10
W = 3.5
So, the equilibrium wage with the subsidy is $3.5 per hour.
To find the quantity of labor, substitute the equilibrium wage into the original labor supply equation:
Qs = 5W
Qs = 5(3.5)
Qs = 17.5
Therefore, the equilibrium wage and quantity of labor with the subsidy are $3.5 and 17.5 workers respectively.
The correct answer is option C: $3.5 and 17.5 workers respectively.