Chapter 8, Problem 10PA

Subpart (a):

To determine

Equilibrium price.

Explanation of Solution

The equilibrium price and the quantity are determined at the interaction of the demand curve and the supply curve of the commodity in the market. When the demand and supply for the commodity are equal at a particular price point, the point will be the equilibrium price level and the equilibrium quantity in the economy.

We have given the supply equation and the demand equations and we can equate them in order to obtain the equilibrium price as follows:

$\begin{array}{c}\text{Supply }=\text{ Demand}\\ \text{2P }=\text{ 300}-\text{P}\\ \text{2P}+\text{P}=300\\ 3\text{P}=300\\ \text{P}=\frac{300}{3}\\ =100\end{array}$

Thus, the equilibrium price is $100. Now we can calculate the equilibrium quantity by substituting the equilibrium price in the equations as follows:

$\begin{array}{c}2\text{P}=300-\text{P}\\ \text{2}\times \text{100}=300-100\\ 200=200\end{array}$

Thus, the equilibrium quantity is 200 units.

Economics Concept Introduction

Concept introduction:

Equilibrium: It is the market equilibrium which is determined by equating the supply to the demand. At this equilibrium point, the supply will be equal to the demand and there will be no excess demand or excess supply in the economy. Thus, the economy will be at equilibrium.

Subpart (b):

To determine

Equilibrium price.

Explanation of Solution

We have given the supply equation and the demand equation changes due to the tax on consumers and the new demand equation is ${\text{Q}}_{\text{D}}=300-\left(\text{P}+\text{T}\right)$ . The equilibrium price and the quantity can be calculated by equating the equations as follows:

$\begin{array}{c}\text{Supply }=\text{ Demand}\\ \text{2P }=\text{ 300}-\left(\text{P}+\text{T}\right)\\ 3\text{P}=300-\text{T}\\ \text{P}=\frac{300-\text{T}}{3}\\ \text{P}=100-\frac{\text{T}}{3}\end{array}$

Thus, the price received by the producers is $100-\frac{\text{T}}{3}$ . The consumers will pay a price which is equal to the price received by the producer plus the tax amount which will be equal to $100+\frac{\text{2T}}{3}$. The quantity sold can be calculated by substituting the price in the equation as follows:

$\begin{array}{c}\text{Q}=300-\left(\text{P}+\text{T}\right)\\ =300-\left(100+\frac{\text{2T}}{3}\right)\\ =200-\frac{2\text{T}}{3}\end{array}$

Thus, the quantity is now $200-\frac{2\text{T}}{3}$.

Economics Concept Introduction

Concept introduction:

Equilibrium: It is the market equilibrium which is determined by equating the supply to the demand. At this equilibrium point, the supply will be equal to the demand and there will be no excess demand or excess supply in the economy. Thus, the economy will be at equilibrium.

Subpart (c):

To determine

Total tax revenue.

Explanation of Solution

We have given that the tax revenue equals to the tax rate multiplied with the quantity. The quantity is calculated in part b as $200-\frac{2\text{T}}{3}$ and the tax revenue can be calculated as follows:

$\begin{array}{c}\text{Tax revenue}=\text{T}\times \text{Q}\\ =\text{T}\times \left(200-\frac{\text{2T}}{3}\right)\\ =\text{200T}-\frac{2{\text{T}}^2}{3}\end{array}$

This relation between the tax revenue can be illustrated as follows:

The graph depicts that the tax revenue will be zero at the tax levels of T = $0 and also at the tax rate of T = $300.

Economics Concept Introduction

Concept introduction:

Tax: It is the unilateral payment made by the public towards the government. There are many different types of taxes in the economy which include the income tax, property tax and professional tax and so forth.

Tax revenue: Tax revenue refers to the total revenue earned by the government through imposing tax.

Subpart (d):

To determine

Deadweight loss.

Explanation of Solution

We have given that deadweight loss is the area of the triangle between the demand and supply curves. The following diagram shows, the area of the triangle (laid on its side) that represents the deadweight loss is 1/2 × base × height, where the base is the change in the price, which is the size of the tax (T) and the height is the amount of the decline in quantity ( $\frac{2\text{T}}{3}$).

The deadweight loss can be calculated as follows:

$\begin{array}{c}\text{Deadweight loss}=\frac{1}{2}\times \text{Size of tax}\times \text{amount of decline in quantity}\\ =\frac{1}{2}\times \text{T}\times \frac{2\text{T}}{3}\\ =\frac{{\text{T}}^2}{3}\end{array}$

Thus, the deadweight loss is equal to $\frac{{\text{T}}^2}{3}$. The relation is illustrated on the graph as follows:

In the above diagram horizontal axis measures quantity and vertical axis measures deadweight loss.

Economics Concept Introduction

Concept introduction:

Tax: It is the unilateral payment made by the public towards the government. There are many different types of taxes in the economy which include the income tax, property tax and professional tax and so forth.

Deadweight loss: It is the reduction in the units where the marginal benefit to the consumer is higher than the marginal cost of production of the unit.

Subpart (e):

To determine

Determine the tax amount.

Explanation of Solution

A tax of $200 will not turn out to be a good policy because the tax revenue decreases when the tax rate reaches to $300 where the tax revenue is zero. The tax revenue is at its maximum at the middle of the tax rate of $0 and $300 which is $150. Thus, in order to increase the tax revenue, the government should reduce the tax rate to $150 from $200 which will be the good alternative policy.

Economics Concept Introduction

Concept introduction:

Tax: It is the unilateral payment made by the public towards the government. There are many different types of taxes in the economy which include the income tax, property tax and professional tax and so forth.