Chapter 7, Problem 6PA

Sub part (a):

To determine

Equilibrium price and quantity.

Explanation of Solution

We have seen the demand schedule and the supply schedule of the consumer and the producer in the former questions. They can be combined together as follows:

Price	Quantity demanded	Quantity supplied
More than $7	0	4
$5 to $7	1	3
$3 to $5	2	2
$1 to $3	3	1
$ or less	4	0

We can form the new table in which the quantity demanded and supplied at price points $2, $4 and $6 can be represented as follows:

Price	Quantity demanded	Quantity supplied
$2	3	1
$4	2	2
$6	1	3

From the above table, we can easily identify that the quantity demanded and the quantity supplied are equal only at the price point of $4. Thus, the equilibrium price is $4 and the equilibrium quantity is 2 bottles of water.

Economics Concept Introduction

Concept introduction:

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 the economy. Thus, the economy will be at equilibrium.

Sub part (b):

To determine

The consumer surplus and the producer surplus of water bottles.

Explanation of Solution

The value that the individual gives to the first bottle of water is $7, whereas the actual price paid by the individual is only $4 which means the individual gets a consumer surplus of $3 from the first bottle that he consumes. For the second bottle, the value that the individual gives is $5 and the price is $4. Here also, he receives the consumer surplus of $1but for the third bottle of water the value to the consumer is only $3, whereas the price is higher than the value and thus, he will not consume beyond 2 bottles. Thus the consumer surplus can be calculated by adding together the consumer surplus from the first bottle and the second bottle as follows:

$\begin{array}{c}{\text{Total consumer surplus at Price}}_{\$4}=\text{Consumer surplus of 1st bottle}+2\text{nd bottle}\\ =3+1\\ =4\end{array}$

Thus, the consumer surplus at price of $4 per bottle of water is $4.

The cost that the seller incurs to the first bottle of water is $1, whereas the actual price paid by the individual is only $4 which means the producer gets a surplus of $3 from the first bottle that he sells. For the second bottle, the value that the individual gives is $4 and the cost is only $3. Here also, he receives the producer surplus of $1. Thus the producer surplus can be calculated by adding together the surplus from the first bottle and the second bottle as follows:

$\begin{array}{c}{\text{Total producer surplus at Price}}_{\$4}=\text{Producer surplus of 1st bottle}+2\text{nd bottle}\\ =3+1\\ =4\end{array}$

Thus, the producer surplus at price of $4 per bottle of water is $4.

Thus, the total surplus of the economy can be calculated by adding the consumer surplus and the producer surplus together as follows:

$\begin{array}{c}\text{Total surplus}=\text{Consumer surplus}+\text{Producer surplus}\\ =4+4\\ =8\end{array}$

Thus, the total surplus is $8.

Economics Concept Introduction

Concept introduction:

Producer surplus: It is the difference between the lowest willing to accept price by the seller and the actual price that the seller receives for the commodity.

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

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 the economy. Thus, the economy will be at equilibrium.

Subpart (c):

To determine

The consumer surplus and the producer surplus of water bottles.

Explanation of Solution

The value that the individual gives to the first bottle of water is $7, whereas the actual price paid by the individual is only $4 which means the individual gets a consumer surplus of $3 from the first bottle that he consumes. Similarly the cost that the seller incurs to the first bottle of water is $1, whereas the actual price paid by the individual is only $4 which means the producer gets a surplus of $3 from the first bottle that he sells.

Thus, if the seller has produced only 1 bottle of water and the consumer had purchased only one bottle of water, each of them would receive a surplus of only $3. The total surplus can be then calculated by summating them together as follows:

$\begin{array}{c}\text{Total surplus}=\text{Consumer surplus}+\text{Producer surplus}\\ =3+3\\ =6\end{array}$

Thus, the total surplus is $6. Thus, with decline in consumption and production by 1 unit, the total surplus declines by $2.

Economics Concept Introduction

Concept introduction:

Producer surplus: It is the difference between the lowest willing to accept price by the seller and the actual price that the seller receives for the commodity.

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

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 the economy. Thus, the economy will be at equilibrium.

Subpart (d):

To determine

Total surplus of water bottles.

Explanation of Solution

When the producer produces 1 more unit of bottle, the cost for him will become $5, whereas the price remains at $4. This means that the total producer surplus will decline by $1 due to the additional cost of production. Then, the total producer surplus will become $3 and it declines by $1.

Similarly, when the consumer consumes 1 more unit of bottle of water, the cost becomes $4, whereas the value from the third bottle to him will be only $3 which means that the consumer surplus will decline by $1 here. Thus, the total decline in the total surplus can be calculated by summating the decline in the producer surplus and the consumer surplus as follows:

$\begin{array}{c}\text{Reduction in total surplus}=\text{Decline in producer surplus}+\text{Decline in consumer surplus}\\ =1+1\\ =2\end{array}$

Thus, the total surplus declines by $2 when the producer produces one more bottle of water and the consumer consumes one more bottle of water.

Economics Concept Introduction

Concept introduction:

Producer surplus: It is the difference between the lowest willing to accept price by the seller and the actual price that the seller receives for the commodity.

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

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 the economy. Thus, the economy will be at equilibrium.