To determine the profit-maximizing output, we need to find the output level where marginal revenue (MR) equals marginal cost (MC). Here’s a step-by-step solution to analyze the given data and identify this point:
1. Review the Given Data:
- Output levels: 5, 10, 15, 20, 25, 30
- Marginal Revenue (MR) for each corresponding output: 100, 150, 175, 205, 285, 390
- Marginal Cost (MC) and Total Cost (TC) are partially provided:
- For Output = 5: TC and MC are given.
- For Output = 10: TC is 50 but MC is missing.
- For Output = 15, 20, 25, 30: MC is missing.
2. Calculate or Estimate Missing Marginal Costs (MC):
Although actual calculations are not shown here, we assume the missing MC values based on given data patterns and economic principles such as the law of diminishing returns (MC typically increases as output increases).
3. Determine the Closest Match of MR and MC:
For each output level, compare the given MR to the MC. The objective is to find where MR and MC are equal or closest:
- Output = 5:
- MR (100) vs. MC (-20) Not optimal; significant difference and negative MC.
- Output = 10:
- MR (150) vs. MC (50) Marginal cost potentially lower than marginal revenue.
- Output = 15:
- MR (175) Marginal cost unknown but inferred higher; likely closer to marginal revenue.
- Output = 20:
- MR (205) Still uncertain in the table data.
- Output = 25:
- MR (285) Possible check, initial high MR suggesting rising MC.
- Output = 30:
- MR (390) Estimatively far higher than achievable expected rising MC.
By evaluating these, we mark the output where the difference between MR and MC is minimal and optimal for profit maximization, preferably pointing towards:
5
Thus, the profit-maximizing output for the firm is the closest recognized match to MR and MC resides within:
5
