The following table represents the MPG corporation's cost of making a gasoline additive. If the selling price of the gasoline additive is $10 per quart, what are the profits of MPG at its profit-maximizing output level?

Quantity

Total Cost

Marginal Cost

0

7

1

16

9

2

24

8

3

31

7

4

39

8

5

49

10

6

61

12

7

75

14

Question

The following table represents the MPG corporation's cost of making a gasoline additive. If the selling price of the gasoline additive is $10 per quart, what are the profits of MPG at its profit-maximizing output level?

Quantity

Total Cost

Marginal Cost

0

7

1

16

9

2

24

8

3

31

7

4

39

8

5

49

10

6

61

12

7

75

14

BlackTom AI · Accepted Answer

To determine the profit-maximizing output under price-taking conditions, we compare marginal cost (MC) to the market price (P).
Option exploration: Since the price is given as $10 per quart, we look for the output level where MC is as close as possible to $10 without exceeding it, because producing an additional unit is worth it only if the revenue from that unit (P) covers its marginal cost.
First, review the marginal costs by quantity:
- MC from 0 to 1: 9
- MC from 1 to 2: 8
- MC from 2 to 3: 7
- MC from 3 to 4: 8
- MC from 4 to 5: 10
- MC from 5 to 6: 12
- MC from 6 to 7: 14
With P = 10, producing up to the point where MC ≤ P is justified. Producing the 5th unit (going from 4 to 5) has MC = 10, which exactly equals price, so this is still profitable.
However, producing the 6th unit (going from 5 to 6) would add MC = 12, which exceeds the price of $10. Therefore, the profit-maximizing output is where MC just does not exceed price, i.e., at q = 5.
Next, compute profit at q = 5: total revenue is P × Q = 10 × 5 = 50. Total cost at Q = 5 is given as 49. Profit = Revenue − Cost = 50 − 49 = 1.
Hence, the profit at the profit-maximizing output is $1. If you review any alternative outputs, note that producing 6 units would lower profit since MC(5→6) = 12 > P, increasing cost more than revenue for that last unit.
In summary, the optimal quantity is 5 quarts, revenue is 50, cost is 49, and profit is 1.

ECON 2010-090 Summer 2025 Econ 2010 Final Exam Summer 2025

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