Answer:
Explanation:
From the information given:
The equilibrium price before tax creates an intersection between the demand and supply.
Qd = 55 -5 P Qs = -50 + 10 P
i.e.
55 - 5P = -50 + 10P
55 + 50 = -5P +10P
110 = 5P
P = 110 / 5
P' = 7
replacing the value of P into the demand equation; we have
Qd = 55 - 5P
Qd = 55 - 5(7)
Qd = 55 - 35
Q' = 20
This tells us that the equilibrium quantity = 20 prior to the equilibrium price which is 7 before tax.
Consumer Surplus = [tex]\dfrac{1}{2} Q' \times (P-P')[/tex]
= [tex]\dfrac{1}{2}\times 20 \times (11 -7)[/tex] (∵ if P is the intercept of the demand and Q is set to be 0, P =11)
Consumer Surplus = 40
Producer surplus = [tex]\dfrac{1}{2}Q^*(P^*-P')[/tex]
here;
P' = y-intercept of supply curve = 5 since we set Qs to be 0
[tex]=\dfrac{1}{2}\times 20 \times (7-5)[/tex]
Producer surplus = 20
Thus prior to commencement of the tax consumer surplus and producer surplus are 40 and 20 respectively.
After-tax:
Qd = 55 - 5p Qs = -60 + 10 P
55 -5 P = -60 + 10 P
115 = 15P
P** = 23/3
Replacing this into the demand
Qd = 55 - 5P
Qd = 55 - 5(23/3)
Qd = 50/3
Thus, after-tax equilibrium quantity = 50/3 and equilibrium pric = 23/3.
Government revenue = (Tax)Q**
Here;
Q** = (P** - P'')
i.e.
P** = after tax equilibrium price
P'' = price suppliers received when Q** is determined in the previous supply curve =20/3
Government Tax revenue = (23/3 - 20/3) × 50/3
Government Tax revenue = 50/3
Dead weight loss = 1/2 × Tax × (Q* - Q**)
Dead weight loss [tex]=\dfrac{1}{2} * (\dfrac{23}{3} -\dfrac{20}{3}) * (20 -\dfrac{250}{3})[/tex]
Dead weight loss = 5/3
