Question

For a perfectly competitive market, daily demand for a good is given by P-10-Q, where P ¡s price and Q is quantity. Supply is given by P = 2 + Q. Suppose the government imposes an excise tax of $2 on sellers in the market. (An excise tax is a tax per unit.) (a) What is the original (before the tax) producer surplus and (b)new (after the tax) producer surplus?

Answer 1

We have the following information

Market demand: P = 10 – Q: When P = 0 Q = 10, and when Q = 0 P = 10

Market supply: P = 2 + Q: When P = 0 Q = –2, and when Q = 0 P = 2

For equilibrium we shall equate demand with supply

10 – Q = 2 + Q

2Q = 8

Equilibrium output = 4

P = 10 – Q

P = 10 – 4

Equilibrium price = $6

Producer Surplus = Area of triangle (ABC)

Producer Surplus = ½ × Base × Height

Producer Surplus = ½ × 4 × 4

Before Tax Producer Surplus = 8

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Now it is given that the government has imposed an excise tax of $2 on sellers in the market.

The new supply curve will be

P_new = P + tax

P_new = (2 + Q) + 2

P_new = 4 + Q

Equating demand with supply

4 + Q = 10 – Q

2Q = 6

Equilibrium (after tax) output = 3

P = 10 – Q

P = 10 – 3

Equilibrium (after tax) price = 7

Producer Surplus = Area of triangle (DEF)

Producer Surplus = ½ × Base × Height

Producer Surplus = ½ × 3 × 3

After Tax Producer Surplus = 4.5

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