Question

a. Suppose the demand function P = 10 - Q, and the supply function is: P = Q, where P is price and Q is quantity. Calculate the equilibrium price and quantity.
b. Suppose government imposes per unit tax of $2 on consumers. The new demand function becomes: P = 8 – Q, while the supply function remains: P = Q. Calculate the new equilibrium price and quantity.
c. Based on (b), calculate the consumer surplus, producer surplus, tax revenue, total surplus and deadweight loss under the tax rate in (b). Also explain your answers in (c) diagrammatically.

Answer 1

(A)

Demand: P=10-Q

Supply: P=Q

At Equilibrium:

Q^D = Q^S

10-P = P

P* = 5

So, Q* = 10-P* = 5

(B)

Tax on consumers: t = $2 per unit

Let price received by seller = P^s

New Demand: P^s+t=10-Q

>> P^s = 8-Q

Supply: P^s = Q

New Equilibrium:

8-P^s = P^s

2P^s = 8

P^s = $4 (This is the price received by the sellers)

Q' = 4

Price paid by Buyers: P^B = (P^s + t) = $6

(C)

For Part A:

Consumer Surplus in Equilibrium:

P_max is the maximum willingness to pay for the good.

P_max = $10

Producer's Surplus in Equilibrium:

P_min is the minimum price at which sellers are willing to supply.

Total Suplus: CS+PS = 12.5+12.5 = 25

For Part B:

Consumer Surplus in Equilibrium:

P_max is the maximum willingness to pay for the good.

P_max = $10, P^B = $6

Producer's Surplus in Equilibrium:

P_min is the minimum price at which sellers are willing to supply.

Tax Revenue Generated:

Total Suplus: CS+PS = 8+8+8 = 24

Deadweight Loss:

Total Surplus in Part A - Total Surplus in Part B = 25-24 = 1

DW LOSS = 1

Lets Look at Consumer Surplus, Producer's Surplus and Deadweight loss through the diagram:

For Part A:

Consumer Surplus: Area AHE = 12.5

Producer's Surplus: Area DHE = 12.5

Total Surplus = Area ADE = 25

For Part B

Consumer Surplus: Area ABF = 8

Producer's Surplus: Area DCG = 8

Tax Revenue: Area BCGF = 8

Total Surplus = Area ADGF = 24

Dead weight Loss: Area FGE = 1