Exhibit 9-8 Consider Exhibit 9-8.What is the profit-maximizing price?

Question

Exhibit 9-8  Consider Exhibit 9-8.What is the profit-maximizing price?

Quizplus · Accepted Answer

To find the profit-maximizing price, we need to look for the highest point on the profit curve, which occurs where the marginal revenue (MR) equals the marginal cost (MC).

Looking at the table, we can calculate the MR by subtracting the change in TR from the previous level of TR. For example, between 2 and 3 units, the TR increases from $30 to $45, so the MR for that unit is $15. Using the same calculation, we can fill in the MR column of the table:

| Q   | TR  | MR  | TC  | Profit |
| --- | --- | --- | --- | ------ |
| 1   | 10  |     | 5   | 5      |
| 2   | 30  | 20  | 14  | 16     |
| 3   | 45  | 15  | 22  | 23     |
| 4   | 52  | 7   | 32  | 20     |
| 5   | 55  | 3   | 42  | 13     |
| 6   | 54  | -1  | 52  | 2      |

To find the MC, we can calculate the change in TC for each unit produced. For example, between 1 and 2 units, the TC increases from $5 to $14, so the MC for that unit is $9. Using the same calculation, we can fill in the MC column of the table:

| Q   | TR  | MR  | TC  | MC  | Profit |
| --- | --- | --- | --- | --- | ------ |
| 1   | 10  |     | 5   |     | 5      |
| 2   | 30  | 20  | 14  | 9   | 16     |
| 3   | 45  | 15  | 22  | 8   | 23     |
| 4   | 52  | 7   | 32  | 10  | 20     |
| 5   | 55  | 3   | 42  | 10  | 13     |
| 6   | 54  | -1  | 52  | 10  | 2      |

We can see that the point where MR=MC is between 2 and 3 units, where the MR is $15 and the MC is $8. Therefore, the profit-maximizing price is the price that corresponds to this quantity, which is:

Price = TR/Q = $45/3 = $15 per unit

To check that this is the correct price, we can calculate the profit at this point:

TR = $45
TC = $22
Profit = TR - TC = $23

This is the highest profit level in the table, so the answer is (C) $23.33, rounded to the nearest cent.