To determine the profit-maximizing quantity for a pure monopoly using the provided table, we need to identify the quantity where marginal revenue (MR) equals marginal cost (MC) and MR is decreasing. Here is a step-by-step analysis:
1. Extract Information from the Table:
- Quantities: 0, 5, 10, 15, 20, 25 (units)
- Marginal Revenue (dollars/unit): - (not given for 0 units), \[tex]$35, \$[/tex]25, \[tex]$15, \$[/tex]5, -\[tex]$5
- Marginal Cost (dollars/unit): - (not given for 0 units), \$[/tex]4, \[tex]$11, \$[/tex]15, \[tex]$18, \$[/tex]20
2. List Relevant Marginal Revenues and Costs:
- At 5 units: MR = \[tex]$35, MC = \$[/tex]4
- At 10 units: MR = \[tex]$25, MC = \$[/tex]11
- At 15 units: MR = \[tex]$15, MC = \$[/tex]15
- At 20 units: MR = \[tex]$5, MC = \$[/tex]18
- At 25 units: MR = -\[tex]$5, MC = \$[/tex]20
3. Identify the Profit-Maximizing Condition:
The profit-maximizing condition occurs where MR = MC and MR is decreasing.
4. Analyze Each Quantity:
- At 5 units: MR = \[tex]$35, MC = \$[/tex]4 (\[tex]$35 > \$[/tex]4)
- At 10 units: MR = \[tex]$25, MC = \$[/tex]11 (\[tex]$25 > \$[/tex]11)
- At 15 units: MR = \[tex]$15, MC = \$[/tex]15 (\[tex]$15 = \$[/tex]15)
- At 20 units: MR = \[tex]$5, MC = \$[/tex]18 (\[tex]$5 < \$[/tex]18)
- At 25 units: MR = -\[tex]$5, MC = \$[/tex]20 (-\[tex]$5 < \$[/tex]20)
5. Conclusion:
The quantity where MR equals MC is at 15 units (MR = \[tex]$15 and MC = \$[/tex]15). At this point, MR is also decreasing, which satisfies the condition for profit maximization.
Therefore, the profit-maximizing quantity for this pure monopoly is 15 units.
