Chapter 7.5, Problem 59E

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 $p=50-0.5x\text{and}p=0.125x$ , 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 59E

Consumer surplus is $\$1600$ and Producer surplus is $\$400$ .

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 40 units and base 80 units.

Therefore, $CS=\frac{1}{2}bh=\frac{1}{2}\times 80\times 40=1600$ .

Similarly, producer surplus (PS) is the triangular region with height 10 units and base 80 units.

Therefore, $PS=\frac{1}{2}bh=\frac{1}{2}\times 80\times 10=400$