Chapter 7.5, Problem 62E

a.

To determine

To graph: The systems of inequalities representing the consumer surplus and producer surplus for the given supply and demand equations.

Explanation of Solution

Given information:

The demand and supply equations are $p=400-0.0002x\text{and}p=225+0.0005x$ , respectively.

Graph:

Using Desmos graphing utility, the graph is shown below:

  

Interpretation:

The region enclosed with blue color represents the solution of the systems of inequalities. It is representing the consumer surplus and producer surplus for the given supply and demand equations.

b.

To determine

To find: The consumer surplus and producer surplus.

Answer to Problem 62E

Consumer surplus is $\$6,250,000$ and Producer surplus is $\$15,625,000$ .

Explanation of Solution

Given information:

Graph that represents the systems of inequalities representing the consumer surplus and producer surplus for the given supply and demand equations:

  

Calculations:

From the graph, we can see that consumer surplus (CS) is the triangular region with height 50 units and base 250000 units.

Therefore, $CS=\frac{1}{2}bh=\frac{1}{2}\times 250000\times 50=6250000$ .

Similarly, producer surplus (PS) is the triangular region with height 125 units and base 250000 units.

Therefore, $PS=\frac{1}{2}bh=\frac{1}{2}\times 250000\times 125=15625000.$