Question

Suppose demand and supply can be characterized by the following equations:

Q_d = 6 – 2P

Q_s = P

Price is in dollars; quantity is in widgets.

For parts (c) and (d), assume a tax of $1.50 per widget sold is imposed on sellers. Show your work for each step below.

C. Find the equilibrium price buyers pay, price sellers get, and quantity algebraically.

D. Calculate the following:

1. consumer surplus
2. producer surplus
3. total firm revenue
4. production costs
5. total tax revenue collected by the government
6. portion of the total tax revenue paid by the buyer
7. portion of the total tax revenue paid by the seller
8. deadweight loss

(e) Does the “law of demand” hold for the demand curve given in this problem? How do you know?

(f) Does the “law of supply” hold for the supply curve given in this problem? How do you know?

Answer 1

The buyers pay a price of $3 per unit and sellers receive a price of $1.5 per unit.

The image below shows the given demand and supply curves

Consumer surplus is the area under the demand curve and above the equilibrium price line (orange) which is equal to:

Producer surplus is the area above the supply curve and under the equilibrium price line (yellow) which is equal to:

Firm's revenue can be calculated by multiplying the equilibrium price by the equilibrium quantity demanded - tax revenue paid to the government which is

Total tax revenue collected by the government is equal to the rectangle (pink) formed after deducting the deadweight loss from this economy which is equal to:

Tax revenue paid by the buyer is

Tax revenue paid by the seller is

Deadweight loss (green) is

The Law of Demand holds for this economy as the demand curve is downward sloping and demand falls as price increases.

The Law of Supply also holds for this economy as the supply curve is upward sloping and supply increases as price increases.