Chapter 7.5, Problem 61E

(a)

To determine

Plot the graph of the consumer surplus and producer surplus for the given equations

Answer to Problem 61E

Graph is shown below

Explanation of Solution

Given:

The demand equation is

  $p=140–0.00002x$

Thesupply equation is

  $p=80+0.00001x$

The point of equilibrium is when,

  $\begin{array}{l}140–0.00002x=80+0.00001x\hfill \\ 0.00002x+0.00001x=140–80\hfill \\ 0.00003x=60\hfill \end{array}$

  $\begin{array}{l}x=\frac{60}{0.00003}\hfill \\ x=2000000\hfill \end{array}$

Therefore ,

  $\begin{array}{l}p=140–0.00002\left(2000000\right) \\ =100\end{array}$

Therefore, the point of equilibrium is $\left(2000000,100\right)$ .

The graph of system representing consumer surplus and producer surplus is shown below.

  

B.)

To determine

Find the consumer surplus and producer surplus.

Answer to Problem 61E

The consumer surplus: $\$40,000,000$

The producer surplus: $\$20,000,000$

Explanation of Solution

Given:

The demand equation is

  $p=140–0.00002x$

The supply equation is

  $p=80+0.00001x$

The consumer surplus is the area on and inside the triangle defined by

  $\begin{array}{l}p\le 140–0.00002x\hfill \\ p\ge 100\hfill \\ x\ge 0\hfill \end{array}$

Therefore, the consumer surplus is the area of the triangle.

Consumer surplus

  $\begin{array}{l}=\frac{1}{2}\left(2000000\right)\left(40\right)\hfill \\ =\$40,000,000\hfill \end{array}$

The producer surplus is the area on and inside the triangle defined by

  $\begin{array}{l}p\ge 80+0.00001x\hfill \\ p\le 100\hfill \\ x\ge 0\hfill \end{array}$

Therefore, the producer surplus is the area of the triangle.

Producer surplus

  $\begin{array}{l}=\frac{1}{2}\left(2000000\right)\left(20\right)\\ =\$20,000,000\end{array}$