Question

Assume the following equation represents the demand for unskilled labor (in thousands of hours per week) in Ohio:

P = (-1/3)Q + 20

     

And the following equation represents the supply of unskilled labor (in thousands of hours per week) in Ohio:

P = (1/2)Q.

What follows is a numeric fill in the blank question with 3 blanks. Now, assume the state government decides it wants to place a $1 tax on labor, with the workers (supply-side) facing the statutory burden of paying the tax. Calculate the new equilibrium quantity of unskilled labor (in thousands of hours per week) after the tax. Q = Blank 1. Fill in the blank, read surrounding text. Calculate the new equilibrium wage the unskilled laborers (per hour) gets to keep after the tax. [Note: this is the amount per hour the workers get to keep and it does NOT include the tax payment they must send to the government] Wage = Calculate the deadweight loss that results from the tax. DWL = .

Answer 1

In the market, equilibrium wage is where demand = supply

(-1/3)Q + 20 = 1/2 Q

5/6 Q = 20 So, Q = 24 P = 1/2Q = 12

The equation changes when tax is levied. The new equilibrium wages and hours can be calculated with th new equation:

(-1/3)Q + 20 = (1/2Q) + 1 (equation of supply + tax amount )

5/6 Q = 19 Q = 22.8   

new equilibrium quantity of unskilled labor (in thousands of hours per week) after the tax = 22,800 hours (blank 1)

Wages after tax = 12 - 1 = $11 (blank 2)

Calculate the deadweight loss that results from the tax. DWL = ½ * 1200 * 1 = $ 600 (blank 3)

[Deadweight loss is calculated by the frmula, ½ * (loss of quantity of unskilled labor due to tax) * (tax amount)]