Answer:
8,000
Step-by-step explanation:
Initially, the market is at equilibrium E1: P = P1; Q = Q1
Assume that the tax is imposed, the market will move to when Q = Q2; the price buyers pay is greater than P1, the price producers receive is less than P1.
We have: Price buyers pay - Price producers receive = Tax
As the tax decreases the equilibrium quantity by 700 headphoes
=> Q1 - Q2 = 700
=> Q2 = Q1 - 700
=> Q1 + Q2 = Q1 + Q1 - 700 = 2Q1 - 700
Before tax:
+) the producer surplus (PS) is equal to the area formed by supply curve S, price line P1 and the vertical axis
=> PS1 = Area of BE1P1
+) the consumer surplus (CS) is equal to the area formed by demand D, price line P1 and the vertical axis
=> CS1 = Area of AE1P1
=> The wellness before tax = CS1 + PS1 = Area of AE1B
After tax:
+) the producer surplus (PS) is equal to the area formed by supply curve S, price line (Price producers receives) and the vertical axis
=> PS2 = Area of BDE
+) the consumer surplus (CS) is equal to the area formed by demand D, price line (price buyers pay) and the vertical axis
=> CS2 = Area of ACF
+) The Tax revenue = Tax * Q2 = (Price buyers pay - Price producers receive) * Q2 = CD * DE = Area of CFDE
=> The wellness after tax = PS2 + CS2 + Tax Revenue = BDE + ACF + CDEF
=> Deadweight loss = Wellness before Tax - Wellness after tax = Area of EFE1 = 2,800
The tax decreases consumer surplus by $4,000.00, and it decreases producer surplus by $6,800.00
So that:
+) CS1 - CS2 = 4,000
=> Area of AE1P1 - Area of ACF = Area of CFE1P1 = 4,000
+) PS1 - PS2 = 6,800
=> Area of BE1P1 - Area of BDE = 6,800
=> Area of EDP1E1 = 6,800
=> Area of CFE1P1 + Area of EDP1E1 = 4,000 + 6,800
=> Area of CFE1ED = 10,800
Area of CDEF + Area of EFE1 = Area of CFE1ED = 10,800
=> Area of CDEF + 2,800 = 10,800
=> Area of CDEF = 8,000
=> Tax revenue = 8,000