Chapter 5, Problem 15PA

To determine

(a)

To calculate the total surplus, when the demand curve is D₁.

Explanation of Solution

The market price at equilibrium is calculated by the intersection of the demand curve and the supply curve.

The demand curve D1 and the supply curve intersect at the point, where the market price is $14.

The total surplus is divided into two parts: Consumer surplus and Producer surplus.

The consumer surplus is represented by the area above the price line and below the demand curve, while the producer surplus is represented by the area under the price line and above the supply curve.

The consumer surplus and producer surplus are shown below:

  $TotalSurplus=ConsumerSurplus+ProducerSurplus$

The consumer surplus is calculated as follows:

  $\begin{array}{l}ConsumerSurplus=\frac{1}{2}\times (22-14)\times (100-0)\\ ConsumerSurplus=\frac{1}{2}\times 8\times 100\\ ConsumerSurplus=400\end{array}$

The producer surplus is calculated as follows:

  $\begin{array}{l}ProducerSurplus=\frac{1}{2}\times (14-6)\times (100-0)\\ ProducerSurplus=\frac{1}{2}\times 8\times 100\\ ProducerSurplus=400\end{array}$

  $\begin{array}{l}TotalSurplus=400+400\\ TotalSurplus=800\end{array}$

To determine

(b)

To calculate the total surplus, when the demand curve is D₂.

Explanation of Solution

The market price at equilibrium is calculated by the intersection of the demand curve and the supply curve.

The demand curve D2 and the supply curve intersect at the point where the market price is $10.

The consumer surplus and producer surplus is shown below:

  $TotalSurplus=ConsumerSurplus+ProducerSurplus$

  $\begin{array}{l}ConsumerSurplus=\frac{1}{2}\times (16-10)\times (50-0)\\ ConsumerSurplus=\frac{1}{2}\times 6\times 50\\ ConsumerSurplus=150\end{array}$

  $\begin{array}{l}ProducerSurplus=\frac{1}{2}\times (10-6)\times (50-0)\\ ProducerSurplus=\frac{1}{2}\times 4\times 50\\ ProducerSurplus=100\end{array}$

  $\begin{array}{l}TotalSurplus=150+100\\ TotalSurplus=250\end{array}$