Applied Calculus for Business: A Project-Based Approach to Business Decision-Making

Subsection 2.5.1 Learn It 5

Subsection 2.5.2 Apply It 5

Subsection 2.5.3 Decision Report 5

In your previous decision (Subsection 2.4.3), your team set an optimal quantity and price for producing your product. At this price point, a maximum amount of profit would be made. However, your solution assumes that every consumer pays the same price for your product. When you set your price point in the previous decision report, there were some consumers who would buy at your price but would have been willing to pay more. The example data below compares one test market to the optimal solution:

            National Quantity   Price   Total Revenue   Total Cost  Total Profit
            q (thousand)        p ($/u) R ($thous)      C ($thous)  P ($thous)

Market #4   1181                299.29  353,457         311,768     41,688
(Optimal)   1262                285.88  360,836         318,678     42,158

If we choose to set a price of \(p = \$285.88\) for our product, we'll sell \(q=1,262\) thousand units. But test market #4 shows that, even at a higher price of \(p = \$299.29\text{,}\) we still would have sold most of those units, \(q = 1,181\) thousand.

If we could identify consumers who were more like those in this test market, and charge them a higher price, we could make additional revenue. This practice is known as price discrimination, and is one factor that helps explain (for example) why gasoline is more expensive on Cape Cod than it is 10 miles away in Plymouth. If we charged the higher price for the first 1,181 thousand units and the lower price for the remaining units, we would still sell all our quantity, but would make an additional revenue of

as shown in the diagrams below. This additional revenue is known as consumer surplus, and if the additional costs of implementing a price discrimination plan are low, this revenue can be largely realized as additional profit.

After your last recommendation, your Vice President of National Sales has come back to your team with a challenge. He's satisfied with your analysis but wants to know if there's any way that a price discrimination scheme could generate an additional $100 million of sales revenue for your product. That additional revenue, he says, could make or break whether your product is approved for production.