1. Calculate the equilibrium price and quantity before the tax is imposed.
The equilibrium occurs where quantity demanded
Qd equals quantity supplied
Qs.
Given the equations:
Qd=500−2P
Qs=3P−200
Set
Qd=Qs:
500−2P=3P−200
Solve for
P:
500+200=3P+2P
700=5P
P=140
Now, substitute
P=140 back into either the demand or supply equation to find
Q:
Using the demand equation:
Qd=500−2(140)=500−280=220
So, the equilibrium price before the tax is $140, and the equilibrium quantity is 220 units.
2. Determine the new equilibrium price and quantity after the tax is imposed.
With a per-unit tax of $10 on the good, the supply equation changes. The new supply function
Qs′ incorporates the tax:
Qs′=3(P−10)−200
Simplify
Qs′:
Qs′=3P−30−200=3P−230
Set
Qd=Qs′ for the new equilibrium:
500−2P=3P−230
Solve for
P:
500+230=3P+2P
730=5P
P=146
Now, find the new equilibrium quantity:
Qd=500−2(146)=500−292=208
The new equilibrium price after the tax is $146, and the new equilibrium quantity is 208 units.
3. Calculate the tax incidence on consumers and producers.
The price consumers pay after the tax is
Pc=146.
The price producers receive after the tax is
Pp=Pc−10=146−10=136.
Tax incidence on consumers (change in price paid by consumers):
ΔPc=Pc−Pinitial=146−140=6
Tax incidence on producers (change in price received by producers):
ΔPp=Pinitial−Pp=140−136=4
4. Determine the deadweight loss resulting from the tax.
Deadweight loss (DWL) is the loss in total surplus due to the tax. It is calculated using the difference in quantity before and after the tax and the tax per unit.
The formula for DWL is:
DWL=21×(Quantity before tax−Quantity after tax)×Tax
DWL=21×(220−208)×10
DWL=21×12×10=60
So, the deadweight loss resulting from the tax is $60.
Summary
- Equilibrium price and quantity before tax: $140 and 220 units.
- New equilibrium price and quantity after tax: $146 and 208 units.
- Tax incidence: $6 on consumers and $4 on producers.
- Deadweight loss: $60
