Chapter 4, Problem 4P

Subpart (a):

To determine

The consumer surplus, total surplus and deadweight loss.

Explanation of Solution

Figure -1 illustrates the market equilibrium that is arrived at equilibrium between the demand and supply curve.

In figure -1 panel (a) and (b), the horizontal axis measures the quantity of bags and the vertical axis measures the price per bag. The curve ‘S’ represents the supply and the curve ‘D’ represents the demand.

The inverse demand function can be derived as follows:

$\begin{array}{c}\text{Price}={\text{Price}}_{\text{At point 'a'}}+\frac{\text{<x-custom-btb-me data-me-id="238" class="microExplainerHighlight">Equilibrium price</x-custom-btb-me>}-{\text{Price}}_{\text{At point 'a'}}}{\text{Q1}-{\text{Quantity}}_{\text{At point 'a'}}}\left(\text{Quantity}\right)\\ =85+\frac{45-85}{20-0}\left(\text{Quantity}\right)\\ =85-2\left(\text{Quantity}\right)\end{array}$

The inverse demand functions of $\text{price}=85-2\left(\text{Quantity}\right)$.

The inverse supply curve can be calculated as follows:

$\begin{array}{c}\text{Price}={\text{Price}}_{\text{At point 'c'}}+\frac{\text{Equilibrium price}-{\text{Price}}_{\text{At point 'c'}}}{\text{Q1}-{\text{Quantity}}_{\text{At point 'c'}}}\left(\text{Quantity}\right)\\ =5+\frac{45-5}{20-0}\left(\text{Quantity}\right)\\ =5+2\left(\text{Quantity}\right)\end{array}$

The inverse supply functions of $\text{price}=5+2\left(\text{Quantity}\right)$.

The inverse demand function and supply functions reveal that the producer willing price is $5 and the consumer willing price is $85. The equilibrium price is $45. The total surplus can be calculated as follows:

$\begin{array}{c}\text{Total surplus}=\frac{1}{2}\left(\begin{array}{l}\text{Consumer willing price}\\ -\text{Producer willing price}\end{array}\right)\times \text{Equilibrium quantity}\\ =\frac{1}{2}\left(85-5\right)\times 20\\ =\left(80\right)\times 10\\ =800\end{array}$

The total surplus is $800.

The consumer surplus can be calculated as follows:

$\begin{array}{c}\text{Consumer surplus}=\frac{1}{2}\left(\begin{array}{l}\text{Consumer willing price}\\ -\text{Equilibrium price}\end{array}\right)\times \text{Equilibrium quantity}\\ =\frac{1}{2}\left(85-45\right)\times 20\\ =\left(40\right)\times 10\\ =400\end{array}$

The consumer surplus is $400.

Economics Concept Introduction

Concept Introduction:

Consumer surplus: It refers to the variation in the probable charge of a product that the consumer intends to pay and the actual price that he has already paid.

Producer surplus: It refers to the variation in the probable price that the producer intends to sell and the actual price that he has already sold.

Subpart (b):

To determine

The consumer surplus, total surplus and deadweight loss.

Explanation of Solution

The consumer willing price at Q2 level of output (15 units) can be calculated by substituting the Q2 level of output to the inverse demand function.

$\begin{array}{c}\text{Price}=85-2\left(\text{15}\right)\\ =85-30\\ =55\end{array}$

The consumer new willing price is $55.

The producer willing price at Q2 level of output (15 units) can be calculated by substituting the Q2 level of output into the inverse supply function.

$\begin{array}{c}\text{Price}=5+2\left(\text{15}\right)\\ =5+30\\ =35\end{array}$

The producer’s new willing price is $35.

The deadweight loss can be calculated as follows:

$\begin{array}{c}\text{Deadweight loss}=\frac{1}{2}\left(\begin{array}{c}\text{Consumer new willing price}\\ -\text{Producer new wlling price}\end{array}\right)\times \left(\begin{array}{c}\text{Equilibrium quantity}\\ -\text{New quantity}\end{array}\right)\\ =\frac{1}{2}\left(55-35\right)\times \left(20-15\right)\\ =\frac{1}{2}\left(20\right)\times \left(5\right)\\ =50\end{array}$

The deadweight loss is $50.

The total surplus can be calculated as follows:

$\begin{array}{c}\text{Total surplus}=\text{Initial total surplus}-\text{Deadweight loss}\\ =800-50\\ =750\end{array}$

The total surplus is $750.

Economics Concept Introduction

Concept Introduction:

Consumer surplus: It refers to the variation in the probable charge of a product that the consumer intends to pay and the actual price that he has already paid.

Producer surplus: It refers to the variation in the probable price that the producer intends to sell and the actual price that he has already sold.

Subpart c):

To determine

The consumer surplus, total surplus and deadweight loss.

Explanation of Solution

The consumer willing price at Q3 level of output (27 units) can be calculated by substituting the Q3 level of output to the inverse demand function.

$\begin{array}{c}\text{Price}=85-2\left(\text{27}\right)\\ =85-54\\ =31\end{array}$

The consumer new willing price is $31.

The producer willing price at Q3 level of output (127 units) can be calculated by substituting the Q3 level of output to the inverse supply function.

$\begin{array}{c}\text{Price}=5+2\left(\text{27}\right)\\ =5+54\\ =59\end{array}$

The producer new willing price is $59.

The deadweight loss can be calculated as follows:

$\begin{array}{c}\text{Deadweight loss}=\frac{1}{2}\left(\begin{array}{c}\text{Consumer new willing price}\\ -\text{Producer new wlling price}\end{array}\right)\times \left(\begin{array}{c}\text{Equilibrium quantity}\\ -\text{New quantity}\end{array}\right)\\ =\frac{1}{2}\left(31-59\right)\times \left(20-27\right)\\ =\frac{1}{2}\left(-28\right)\times \left(-7\right)\\ =98\end{array}$

The deadweight loss is $98.

The total surplus can be calculated as follows:

$\begin{array}{c}\text{Total surplus}=\text{Initial total surplus}-\text{Deadweight loss}\\ =800-98\\ =702\end{array}$

The total surplus is $702.

Economics Concept Introduction

Concept Introduction:

Consumer surplus: It refers to the variation in the probable charge of a product that the consumer intends to pay and the actual price that he has already paid.

Producer surplus: It refers to the variation in the probable price that the producer intends to sell and the actual price that he has already sold.