Chapter 50, Problem 3CYU

a)

To determine

Equilibrium price and equilibrium quantity after excise tax.

Explanation of Solution

Without the excise tax, A, R, EM, and Ed sell, and H, B, L, and M buy

one can of soda each at a price of $0.40 per can. And, the total quantity bought and sold is 4. Therefore, the equilibrium price is $0.40 per can, and the equilibrium quantity is 4.

Economics Concept Introduction

Introduction: A tax that is levied on the sale of certain goods by the government is called an excise tax.

When the supply of goods matches the demand for the good, then this is the situation of equilibrium price or equilibrium quantity.

b)

To determine

Quantity after excise tax

Explanation of Solution

With the excise tax, A and R sell, and H and B buy one can of soda each, and therefore, the

quantity sold would be 2.

Economics Concept Introduction

Introduction: A tax that is levied on the sale of certain goods by the government is called an excise tax.

Quantity is the number of goods that are sold or supplied in the market.

c)

To determine

Consumer surplus for each consumer with and without tax and total lost consumer surplus.

Explanation of Solution

  $\begin{array}{l}\text{Without the excise tax, H’s consumer surplus is:}\hfill \\ =\$0.70-\$0.40\hfill \\ =\$0.30,\hfill \\ \text{Bart’s consumer surplus is:}\hfill \\ =\$0.60-\$0.40\hfill \\ =\$0.20,\hfill \\ \text{Lisa’s consumer surplus is:}\hfill \\ =\$0.50-\$0.40\hfill \\ =\$0.10,\hfill \\ \text{And Marge’s consumer surplus would be:}\hfill \\ =\$0.40-\$0.40\hfill \\ =\$\mathrm{0.00.}\hfill \\ \text{Therefore, the total consumer surplus is}\hfill \\ =\$0.30+\$0.20+\$0.10+\$0.00\hfill \\ =\$\mathrm{0.60.}\hfill \end{array}$

  $\begin{array}{l}\text{Then, with the tax, H’s consumer surplus is:}\hfill \\ =\$0.70-\$0.60\hfill \\ =\$0.10\hfill \\ \text{Bart’s consumer surplus is}\hfill \\ =\$0.60-\$0.60\hfill \\ =\$\mathrm{0.00.}\hfill \\ \text{Therefore, the total consumer surplus post-tax is}\hfill \\ =\$0.10+\$0.00\hfill \\ =\$\mathrm{0.10.}\hfill \end{array}$

  $\begin{array}{l}\text{And, here, due to tax, the total consumer surplus which is lost is:}\hfill \\ \text{= Total consumer surplus pre-tax}-\text{total consumer surplus post-tax}\hfill \\ =\$0.60-\$0.10\hfill \\ =\$0.50\hfill \end{array}$

Economics Concept Introduction

Introduction: A tax that is levied on the sale of certain goods by the government is called an excise tax.

Any excess in production, earnings, or the supply of goods is called surplus which is more than the need.

d)

To determine

Producer surplus for each producer with and without tax and total lost producer surplus.

Explanation of Solution

  $\begin{array}{l}\text{Without the excise tax, A’s producer surplus is:}\hfill \\ \text{= \$0}\text{.40 }-\text{ \$0}\text{.10}\hfill \\ \text{= \$0}\text{.30,}\hfill \\ \text{Rosalie’s producer surplus is:}\hfill \\ \text{= \$0}\text{.40 }-\text{ \$0}\text{.20}\hfill \\ \text{= \$0}\text{.20,}\hfill \\ \text{EM’s producer surplus is:}\hfill \\ \text{= \$0}\text{.40 }-\text{ \$0}\text{.30}\hfill \\ \text{= \$0}\text{.10,}\hfill \\ \text{And, Ed’s producer surplus is:}\hfill \\ \text{= \$0}\text{.40 }-\text{ \$0}\text{.40}\hfill \\ \text{= \$0}\text{.00}\text{.}\hfill \\ \text{Therefore, Total producer surplus is:}\hfill \\ \text{= \$0}\text{.30 + \$0}\text{.20 + \$0}\text{.10 + \$0}\text{.00}\hfill \\ \text{= \$0}\text{.60}\text{.}\hfill \end{array}$

  $\begin{array}{l}\text{Then, With the tax, A’s producer surplus is:}\hfill \\ \text{= \$0}\text{.20}-\text{\$0}\text{.10}\hfill \\ \text{= \$0}\text{.10}\hfill \\ \text{and R’s producer surplus is:}\hfill \\ \text{= \$0}\text{.20}-\text{\$0}\text{.20}\hfill \\ \text{= \$0}\text{.00}\text{.}\hfill \\ \text{Therefore, total producer surplus post-tax is:}\hfill \\ \text{= \$0}\text{.10 + \$0}\text{.00}\hfill \\ \text{= \$0}\text{.10}\text{.}\hfill \end{array}$

  $\begin{array}{l}\text{And, here, as a result of tax, the total producer surplus lost is:}\hfill \\ =\$0.60-\$0.10\hfill \\ =\$\mathrm{0.50.}\hfill \end{array}$

Economics Concept Introduction

Introduction: A tax that is levied on the sale of certain goods by the government is called an excise tax.

Any excess in production, earnings, or the supply of goods is called surplus which is more than the need.

e)

To determine

Government revenue that excise tax creates

Explanation of Solution

From the selling of two cans of soda after imposing excise tax, therefore, the tax revenue of the government from this excise tax would be:

  $\begin{array}{l}=2\times \$0.40\hfill \\ =\$0.80\hfill \end{array}$

Economics Concept Introduction

Introduction: A tax that is levied on the sale of certain goods by the government is called an excise tax.

f)

To determine

Deadweight loss from the imposition of tax

Explanation of Solution

  $\begin{array}{l}\text{Without tax total surplus is:}\hfill \\ \text{= \$0}\text{.60 + \$0}\text{.60}\hfill \\ \text{= \$1}\text{.20}\text{.}\hfill \\ \text{With the tax, total surplus is:}\hfill \\ \text{= \$0}\text{.10 + \$0}\text{.10}\hfill \\ \text{= \$0}\text{.20,}\hfill \\ \text{and government tax revenue is \$0}\text{.80}\text{.}\hfill \\ \text{Therefore, deadweight loss from this excise tax is:}\hfill \\ \text{= \$1}\text{.20–}\left(\text{\$0}\text{.20+\$0}\text{.80}\right)\hfill \\ \text{= \$0}\text{.20}\hfill \end{array}$

Economics Concept Introduction

Introduction: When supply and demand are out of equilibrium, then there is deadweight loss due to market inefficiency.