Question

Suppose demand is given by teh equation PD= 100-2QD and supply is given by the equation PS=50+ 3Qs. Price is measured in dollars and quantity is measured in units, What is the deadweight loss of $20?

a. 40
b. 60
c. 20
d. 80

Answer 1

a. $40

Step-by-step explanation:

Question "What is the deadweight loss of $20 tax"

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