Chapter 7, Problem 80RE

a.

To determine

To find Consumer Surplus and Producer Surplus.

Answer to Problem 80RE

The equilibrium point is $\boxed{x,p=\left(200000,90\right)}$

Explanation of Solution

Given information:

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

  $\begin{array}{l}Demand\\ P=130-0.0002x\end{array}$  $\begin{array}{l}Supply\\ P=30+0.0003x\end{array}$

Calculation:

Consider the given demand and supply equations,

  $\begin{array}{l}P=130-0.0002x\mathrm{.....}\left(1\right)\\ P=30+0.0003x\mathrm{.....}\left(2\right)\end{array}$

Now find the equilibrium point is the intersection point of given two equations.

Equate both the equations,

  $\begin{array}{l}130-0.0002x=30+0.0003x\\ -0.0002x-0.0003x=-130+30\\ -0.0005x=-100\\ x=\frac{100}{0.0005}=200,000\\ x=200,000\end{array}$

Substitute $x=200,000$ in equation $\left(1\right)$

  $\begin{array}{l}p=130-0.0002\left(200,000\right)\\ =130-40\\ p=90\end{array}$

Hence, the equilibrium point is $\boxed{x,p=\left(200000,90\right)}$

Now the graph is,

  

Hence, the graph is as show.

b.

To determine

To find Consumer Surplus and Producer Surplus.

Answer to Problem 80RE

Consumer and producer surplus is $\boxed{\$4,000,000}$ , $\boxed{\$6,000,000}$

Explanation of Solution

Given information:

Find the consumer surplus and producer surplus.

  $\begin{array}{l}Demand\\ P=130-0.0002x\end{array}$  $\begin{array}{l}Supply\\ P=30+0.0003x\end{array}$

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,

  $\begin{array}{l}=\frac{1}{2}\left(200000\right)\left(40\right)\\ =\$4,000,000\end{array}$

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

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

Producer surplus,

  $\begin{array}{l}=\frac{1}{2}\left(200000\right)\left(60\right)\\ =\$6,000,000\end{array}$

Hence, consumer and producer surplus is $\boxed{\$4,000,000}$ , $\boxed{\$6,000,000}$