Chapter 9, Problem 8PA

Subpart (a):

To determine

The equilibrium price and the quantity of haircuts and total surplus.

Explanation of Solution

Demand curve: The demand equation is ${\text{Q}}^{\text{D}}=\text{8}-\text{p}$ indicates that the consumer maximum willing price is $8 (When quantity is zero) and their maximum willing to buy the good is 8 units (when the price is zero). Connecting these points $\left(\left(8,0\right)\text{ and }\left(0,8\right)\right)$ gives demand curve.

Supply curve: The supply equation is ${\text{Q}}^{\text{S}}=\text{p}$ indicates that producer minimum willing price is zero (When quantity is zero) and producer willing to sell 1 unit for increasing price by 1 unit. Thus, draw extent the line from these points $\left(\left(0,0\right)\text{ and }\left(1,\text{ 1}\right)\right)$ would give supply curve. The market equilibrium is drawn based on the above information as mentioned in Figure 1.

In Figure 1, horizontal axis measures quantity and vertical axis measures price. The curve D indicates demand and the curve S indicates supply. Market reaches the equilibrium at point ‘e’ where the demand curve intersects with supply curve.

Equilibrium price can be calculated as follows.

$\begin{array}{c}\text{Demand}=\text{Supply}\\ \text{8}-\text{p}=\text{p}\\ \text{2p}=8\\ \text{p}=\frac{8}{2}\\ =4\end{array}$

Equilibrium price is $4.

Equilibrium quantity can be calculated by substituting the equilibrium price in to supply equation.

$\begin{array}{c}\text{Q}=\text{p}\\ =4\end{array}$

Thus, equilibrium quantity is 4 units.

Consumer surplus can be calculated as follows.

$\begin{array}{c}\text{Consumer suplus}=\frac{1}{2}\times \left(\begin{array}{l}\text{Maximum willing price}\\ -\text{Equilibrium price}\end{array}\right)\times \left(\text{Equilibrium quantity}\right)\\ =\frac{1}{2}\times \left(\text{8}-\text{4}\right)\times \left(\text{4}\right)\\ =8\end{array}$

Consumer surplus is $8.

Producer surplus can be calculated as follows.

$\begin{array}{c}\text{Producer suplus}=\frac{1}{2}\times \left(\begin{array}{l}\text{Equilibrium price}\\ -\text{Miniimum willing price}\end{array}\right)\times \left(\text{Equilibrium quantity}\right)\\ =\frac{1}{2}\times \left(4-0\right)\times \left(\text{4}\right)\\ =8\end{array}$

Producer surplus is $8.

Total surplus can be calculated as follows.

$\begin{array}{c}\text{Total surplus}=\text{Consumer surplus}+\text{Proudcer surplus}\\ =8+8\\ =16\end{array}$

Total surplus is $16.

Economics Concept Introduction

Concept introduction:

Consumer surplus: It is the difference between the highest willing price of the consumer and the actual price that the consumer pays.

Producer surplus: It is the difference between the minimum accepted price for the producer and the actual price received by the producer.

Equilibrium price:  It is the market price 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 an economy. Thus, the economy will be at equilibrium.

Subpart (b):

To determine

The equilibrium price and the quantity of haircuts and total surplus.

Explanation of Solution

The world price for the good is $1. Thus, when the country opens the market for trade, the price becomes $1 in domestic country too. Figure 2 describe this situation.

In Figure 2, horizontal axis measures quantity and vertical axis measures price. The curve D indicates demand and the curve S indicates supply. Market reaches the equilibrium at point ‘e’ where the demand curve intersects with supply curve.

When the competitor (Rest of the world) sells a good at price $1, in domestic country equilibrium price become equal to world price. Thus, equilibrium price in the domestic country is $1.

Equilibrium domestic supply can be calculated by substituting the domestic equilibrium price in to supply equation.

$\begin{array}{c}\text{Q}=\text{p}\\ =1\end{array}$

Thus, equilibrium quantity is 1 unit.

Equilibrium domestic demand can be calculated by substituting the domestic equilibrium price in to demand equation.

$\begin{array}{c}\text{Q}=8-\text{p}\\ =8-1\\ =7\end{array}$

Thus, equilibrium domestic demand is 7 units.

Total imports can be calculated as follows.

$\begin{array}{c}\text{Imports}=\text{Domestic demand}-\text{Domestic supply}\\ =7-1\\ =6\end{array}$

Domestic imports are 6 units.

Consumer surplus can be calculated as follows.

$\begin{array}{c}\text{Consumer suplus}=\frac{1}{2}\times \left(\begin{array}{l}\text{Maximum willing price}\\ -\text{Equilibrium price}\end{array}\right)\times \left(\text{Equilibrium quantity}\right)\\ =\frac{1}{2}\times \left(\text{8}-\text{1}\right)\times \left(\text{7}\right)\\ =24.5\end{array}$

Consumer surplus is $24.5.

Producer surplus can be calculated as follows.

$\begin{array}{c}\text{Producer suplus}=\frac{1}{2}\times \left(\begin{array}{l}\text{Equilibrium price}\\ -\text{Miniimum willing price}\end{array}\right)\times \left({\text{Quantity}}_{\text{Supply}}\right)\\ =\frac{1}{2}\times \left(1-0\right)\times \left(\text{1}\right)\\ =0.5\end{array}$

Producer surplus is $0.5.

Total surplus can be calculated as follows.

$\begin{array}{c}\text{Total surplus}=\text{Consumer surplus}+\text{Proudcer surplus}\\ =24.5+0.5\\ =25\end{array}$

Total surplus is $25.

Economics Concept Introduction

Concept introduction:

Consumer surplus: It is the difference between the highest willing price of the consumer and the actual price that the consumer pays.

Producer surplus: It is the difference between the minimum accepted price for the producer and the actual price received by the producer.

Equilibrium price:  It is the market price 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 an economy. Thus, the economy will be at equilibrium.

Subpar (c):

To determine

The equilibrium price and the quantity of haircuts and total surplus.

Explanation of Solution

When domestic country impose tariff of $1, the price in domestic country increases from $1 to $2. This increase in price is shown in the Figure 3.

In Figure 3, horizontal axis measures quantity and vertical axis measures price. The curve D indicates demand and the curve S indicates supply. Market reaches the equilibrium at point ‘e’ where the demand curve intersects with supply curve. Price is increases from $1 to $2 due to the tariff of $1.

Domestic equilibrium price can be calculated as follows.

$\begin{array}{c}\text{New price}=\text{Initial price}+\text{Tariff}\\ =1+1\\ =2\end{array}$

New domestic price is $2.

Equilibrium domestic supply can be calculated by substituting the domestic equilibrium price in to supply equation.

$\begin{array}{c}\text{Q}=\text{p}\\ =2\end{array}$

Thus, equilibrium quantity is 2 units.

Equilibrium domestic demand can be calculated by substituting the domestic equilibrium price in to demand equation.

$\begin{array}{c}\text{Q}=8-\text{p}\\ =8-2\\ =6\end{array}$

Thus, equilibrium domestic demand is 6 units.

Total imports can be calculated as follows.

$\begin{array}{c}\text{Imports}=\text{Domestic demand}-\text{Domestic supply}\\ =6-2\\ =4\end{array}$

Domestic imports are 4 units.

Consumer surplus can be calculated as follows.

$\begin{array}{c}\text{Consumer suplus}=\frac{1}{2}\times \left(\begin{array}{l}\text{Maximum willing price}\\ -\text{Equilibrium price}\end{array}\right)\times \left(\text{Equilibrium quantity}\right)\\ =\frac{1}{2}\times \left(\text{8}-\text{2}\right)\times \left(\text{6}\right)\\ =18\end{array}$

Consumer surplus is $18.

Producer surplus can be calculated as follows.

$\begin{array}{c}\text{Producer suplus}=\frac{1}{2}\times \left(\begin{array}{l}\text{Equilibrium price}\\ -\text{Miniimum willing price}\end{array}\right)\times \left({\text{Quantity}}_{\text{Supply}}\right)\\ =\frac{1}{2}\times \left(2-0\right)\times \left(\text{2}\right)\\ =2\end{array}$

Producer surplus is $2.

Government revenue can be calculated as follows.

$\begin{array}{c}\text{Government revenue}={\text{Tariff}}_{\text{Per unit}}\times {\text{Quantity}}_{\text{Imports}}\\ =1\times 4\\ =4\end{array}$

Government revenue is 4.

Total surplus can be calculated as follows.

$\begin{array}{c}\text{Total surplus}=\text{Consumer surplus}+\text{Proudcer surplus+Government revenue}\\ =18+2+4\\ =24\end{array}$

Total surplus is $24.

Economics Concept Introduction

Concept introduction:

Consumer surplus: It is the difference between the highest willing price of the consumer and the actual price that the consumer pays.

Producer surplus: It is the difference between the minimum accepted price for the producer and the actual price received by the producer.

Equilibrium price:  It is the market price 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 an economy. Thus, the economy will be at equilibrium.

Subpart (d):

To determine

Calculate total gains and deadweight loss.

Explanation of Solution

Total gains from opening up trade can be calculated as follows.

$\begin{array}{c}\text{Total gains from trade}={\text{Total surplus}}_{\text{After tariff}}-{\text{Total surplus}}_{\text{Closed economy}}\\ =24-16\\ =8\end{array}$

Total gains are$8.

Deadweight loss can be calculated as follows.

$\begin{array}{c}\text{Deadweight loss}={\text{Total surplus}}_{\text{Before tariff}}-{\text{Total surplus}}_{\text{After tariff}}\\ =25-24\\ =1\end{array}$

Deadweight loss is $1.