Chapter 7, Problem 79RE

a.

To determine

To find Consumer Surplus and Producer Surplus.

Answer to Problem 79RE

The equilibrium point is $\boxed{x,p=\left(00000,130\right)}$

Explanation of Solution

Given information:

Graph the systems representing the consumer surplus and producer surplus for the supply and demand equations

  $\begin{array}{l}Demand\\ P=160-0.0001x\end{array}$  $\begin{array}{l}Supply\\ P=70+0.0002x\end{array}$

Calculation:

Consider the given demand and supply equations,

  $\begin{array}{l}Demand\\ P=160-0.0001x\end{array}$

  $\begin{array}{l}Supply\\ P=70+0.0002x\end{array}$

Now plot the graph of demand and supply.

The equilibrium point is $\boxed{x,p=\left(00000,130\right)}$

  

Hence, the graph is as show.

b.

To determine

To find Consumer Surplus and Producer Surplus.

Answer to Problem 79RE

Consumer and producer surplus is $\boxed{\$4,500,000}$ , $\boxed{\$9,000,000}$

Explanation of Solution

Given information:

Find the consumer surplus and producer surplus.

  $\begin{array}{l}Demand\\ P=160-0.0001x\end{array}$  $\begin{array}{l}Supply\\ P=70-0.0002x\end{array}$

Calculation:

Consider the graph of part $\left(a\right)$ , consumer surplus is considered as area occupied by consumer surplus region.

Area of the triangle, $=\frac{1}{2}bh$

Consumer surplus,

  $\begin{array}{l}=\frac{1}{2}\left(300000\right)\left(160-130\right)\\ =150000\times 30\\ =\$4,500,000\end{array}$

Producer surplus is considered as area occupied by producer surplus region.

Area of the triangle, $=\frac{1}{2}bh$

Producer surplus,

  $\begin{array}{l}=\frac{1}{2}\left(300000\right)\left(130-70\right)\\ =150000\times 60\\ =\$9,000,000\end{array}$

Hence, consumer and producer surplus is $\boxed{\$4,500,000}$ , $\boxed{\$9,000,000}$