Answer:
a. $40
Explanation:
Question <em>"What is the deadweight loss of $20 tax"</em>
Demand is given by PD = 100 - 2QD
supply is given by PS = 50 + 3QS
For equilibrium, Demand = Supply
100 - 2QD = 50 + 3QS
3QS + 2QD = 100 - 50
5Q= 50
Q = 10 units (Equilibrium quantity)
From PD = 100 - 2QD
P = 100 - (2*10)
P= $80 (equilibrium price)
With a tax of $20, the new supply curve is (PS - 20) = 50 + 3QS
PS = 550 + 20 + 3QS
PS = 70 + 3QS
Then, the new equilibrium is Demand = New supply
100-2Q = 70+3Q
3Q + 2Q = 100 - 70
5Q = 30
Q = 6 units (New equilibrium quantity)
P = = 70+3Q
P = 70 + (3*6) = $88 (New equilibrium price)
P = $88
Now, at the new equilibrium quantity (6 units), Price on the initial supply curve, PS = 50+(3*6) = $68.
Then, the deadweight loss = 1/2* (Equilibrium quantity - New equilibrium quantity) * (New equilibrium price - Price on initial supply curve at new equilibrium quantity)
Deadweight loss = 1/2*(10-6)*(88-68)
Deadweight loss = 1/2*4*20
Deadweight loss = $40
