- Marginal revenue is defined as the change in total revenue when production increases by one unit.
- According to the table, the marginal revenue is constant at \(\$10\) for all production levels from 1 to 7 pies.
- Because the value remains constant at \(\$10\), it does not decrease as production increases.
- Therefore, the statement that marginal revenue decreases by ten dollars is \(\boxed{\text{False}}\).
Explanation
- Understanding Marginal Revenue
The problem asks us to evaluate a statement about the marginal revenue based on the provided table. Marginal revenue is defined as the additional revenue generated from the sale of one additional unit of output. Mathematically, for a given quantity of production \(n\), the marginal revenue \(MR_n\) is given by the difference in total revenue between producing \(n\) units and \(n-1\) units: \[MR_n = TR_n - TR_{n-1}\] The provided table lists the total revenue and the marginal revenue for each number of pies produced from 1 to 7.
- Analyzing the Table Data
By observing the "Marginal revenue" column in the table, we can see that for every unit of production from 1 to 7, the marginal revenue is consistently \(10\). Specifically:
- At 1 pie, \(MR = \$10\)
- At 2 pies, \(MR = \$10\)
- At 3 pies, \(MR = \$10\)
- At 4 pies, \(MR = \$10\)
- At 5 pies, \(MR = \$10\)
- At 6 pies, \(MR = \$10\)
- At 7 pies, \(MR = \$10\)
Since the value is constant, the marginal revenue does not change as production increases. Therefore, the statement "the marginal revenue decreases by ten dollars as production increases" is false. The marginal revenue remains constant at \(\$10\).
- Conclusion
The statement "the marginal revenue decreases by ten dollars as production increases" is clearly incorrect because the table shows that marginal revenue is constant at \(\$10\). Therefore, the correct conclusion is that the marginal revenue does not decrease; it remains constant. Since the question provides a specific multiple-choice format, the correct answer is that the statement is false.
Examples
In a competitive market, a firm is often a "price taker," meaning it can sell any quantity of a product at a constant market price. In this scenario, every additional unit sold adds the same amount to the total revenue, making the marginal revenue constant. For example, if a farmer sells apples for \(\$2\) each, the marginal revenue for every additional apple sold is consistently \(\$2\), regardless of whether they have sold 10 or 100 apples. This demonstrates how marginal revenue reflects the price consistency in a perfectly competitive market.