Math Problem Statement
The columns are labeled (1) Total product (output); (2) average fixed cost (AFC) in dollars; (3) average variable cost (AVC) in dollars; (4) average total cost (ATC) in dollars; (5) marginal cost (MC) in dollars; (6) Price equals marginal revenue (MR) (7) in dollars; and total economic profit (positive) or loss (negative) in dollars. The data is as follows: 0, blank, blank, blank, blank, blank, blank, Negative 100. 1, 100.00, 90.00, 190.00, 90, 131, and negative 59. 2, 50.00, 85.00, 135.00, 80, 131, and negative 8. 3, 33.33, 80.00, 113.33, 70, 131, and positive 53. 4, 25.00, 75.00, 100.00, 60, 131, and positive 124.
5, 20.00, 74.00, 94.00, 70, 131, and positive 185. 6, 16.67, 75.00, 91.67, 80, 131, and positive 236. 7, 14.29, 77.14, 91.43, 90, 131, and positive 277. 8, 12.50, 81.25, 93.75, 110, 131, and positive 298. 9, 11.11, 86.67, 97.78, 130, 131, and positive 299. 10, 10.00, 93.00, 103.00, 150, 131, and positive 280.Select all that apply
Based on the information given in the table, which of the following statements are true?
Multiple select question.
The average fixed cost increases after the sixth unit of production.
The tenth unit should be produced as it adds more to revenue than to cost.
Every unit of output up to and including the ninth unit represents greater marginal revenue than marginal cost.
The ninth unit of output is the profit-maximizing level of output.Second last data row with the total product, 9 is highlighted.
Solution
Let’s go through each statement systematically using the data provided.
1. The average fixed cost increases after the sixth unit of production.
- False. Average Fixed Cost (AFC) consistently decreases as production increases. For example, AFC at 6 units is 16.67, and at 7 units, it is 14.29, then it continues decreasing. There’s no increase in AFC after the sixth unit of production.
2. The tenth unit should be produced as it adds more to revenue than to cost.
- False. For the tenth unit, Marginal Revenue (MR) = 131 and Marginal Cost (MC) = 150. Since the cost added by producing the tenth unit (150) exceeds the revenue it generates (131), the tenth unit does not add more to revenue than to cost. It would actually reduce profit.
3. Every unit of output up to and including the ninth unit represents greater marginal revenue than marginal cost.
- True. From the data, we can see that for every unit from 1 to 9, MR (131) is greater than MC. For example:
- 1st unit: MC = 90, MR = 131.
- 9th unit: MC = 130, MR = 131. In all cases, MR is greater than MC up to and including the ninth unit.
4. The ninth unit of output is the profit-maximizing level of output.
- True. The ninth unit of output is the last unit where MR > MC (MR = 131, MC = 130). At the tenth unit, MC exceeds MR, which means that profit decreases beyond the ninth unit. Therefore, the ninth unit represents the profit-maximizing output level.
Summary:
- The true statements are:
- Every unit of output up to and including the ninth unit represents greater marginal revenue than marginal cost.
- The ninth unit of output is the profit-maximizing level of output.
Would you like more details or have any questions?
Here are 5 related questions for further exploration:
- What happens to profit if production goes beyond the profit-maximizing level?
- How is Average Fixed Cost (AFC) calculated for each unit of output?
- Can a company continue operating at a loss in the short run?
- Why is Marginal Cost (MC) important in determining the profit-maximizing output?
- What is the relationship between Average Total Cost (ATC) and Marginal Cost (MC)?
Tip: Always compare Marginal Cost (MC) and Marginal Revenue (MR) to determine the optimal output level where profit is maximized!
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Math Problem Analysis
Mathematical Concepts
Cost Analysis
Profit Maximization
Marginal Analysis
Formulas
Average Fixed Cost (AFC) = Total Fixed Costs / Output
Marginal Cost (MC) = Change in Total Cost / Change in Output
Profit Maximization: Produce where MR = MC
Theorems
Profit is maximized when Marginal Revenue equals Marginal Cost (MR = MC)
Suitable Grade Level
Grades 11-12 (Economics, Business Mathematics)