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Sagot :
To determine the profit-maximizing level of output for a monopolistically competitive firm, we need to find the quantity where Marginal Revenue (MR) equals Marginal Cost (MC). Here is a step-by-step solution:
1. Understand the data from the table:
- Quantity: [0, 1, 2, 3, 4, 5, 6, 7, 10]
- Price: [[tex]$50, $[/tex]45, [tex]$40, $[/tex]35, [tex]$30, $[/tex]25, [tex]$20, $[/tex]15, [tex]$5] - Marginal Cost: [None, $[/tex]30, [tex]$24, $[/tex]14, [tex]$10, $[/tex]12, [tex]$32, $[/tex]10, [tex]$140] - Average Total Cost: [None, $[/tex]40, [tex]$32, $[/tex]26, [tex]$22, $[/tex]20, [tex]$22, $[/tex]30, [tex]$50] 2. Calculate Total Revenue (TR): - TR = Price * Quantity - TR for Quantity 0: $[/tex]50 * 0 = [tex]$0 TR for Quantity 1: $[/tex]45 * 1 = [tex]$45 TR for Quantity 2: $[/tex]40 * 2 = [tex]$80 TR for Quantity 3: $[/tex]35 * 3 = [tex]$105 TR for Quantity 4: $[/tex]30 * 4 = [tex]$120 TR for Quantity 5: $[/tex]25 * 5 = [tex]$125 TR for Quantity 6: $[/tex]20 * 6 = [tex]$120 TR for Quantity 7: $[/tex]15 * 7 = [tex]$105 TR for Quantity 10: $[/tex]5 * 10 = [tex]$50 3. Calculate Marginal Revenue (MR): - MR is the change in Total Revenue (TR) divided by the change in quantity. MR for Quantity 1: (TR for 1 - TR for 0) / (1 - 0) = ($[/tex]45 - [tex]$0) / 1 = $[/tex]45
MR for Quantity 2: (TR for 2 - TR for 1) / (2 - 1) = ([tex]$80 - $[/tex]45) / 1 = [tex]$35 MR for Quantity 3: (TR for 3 - TR for 2) / (3 - 2) = ($[/tex]105 - [tex]$80) / 1 = $[/tex]25
MR for Quantity 4: (TR for 4 - TR for 3) / (4 - 3) = ([tex]$120 - $[/tex]105) / 1 = [tex]$15 MR for Quantity 5: (TR for 5 - TR for 4) / (5 - 4) = ($[/tex]125 - [tex]$120) / 1 = $[/tex]5
MR for Quantity 6: (TR for 6 - TR for 5) / (6 - 5) = ([tex]$120 - $[/tex]125) / 1 = -[tex]$5 MR for Quantity 7: (TR for 7 - TR for 6) / (7 - 6) = ($[/tex]105 - [tex]$120) / 1 = -$[/tex]15
MR for Quantity 10: (TR for 10 - TR for 7) / (10 - 7) = ([tex]$50 - $[/tex]105) / 3 = -[tex]$18.3 4. Compare Marginal Cost (MC) and Marginal Revenue (MR): - For profit maximization, we find the quantity at which MR = MC: - For Quantity 1: MR = $[/tex]45, MC = [tex]$30 (MR > MC) - For Quantity 2: MR = $[/tex]35, MC = [tex]$24 (MR > MC) - For Quantity 3: MR = $[/tex]25, MC = [tex]$14 (MR > MC) - For Quantity 4: MR = $[/tex]15, MC = [tex]$10 (MR > MC) - For Quantity 5: MR = $[/tex]5, MC = [tex]$12 (MR < MC) At Quantity 1, MR equals $[/tex]45 and MC equals $30. When MR = MC, the firm maximizes its profit. Therefore, the firm's profit-maximizing level of output is:
[tex]\[ \boxed{1 \text{ unit of output}} \][/tex]
Thus, the answer is:
None of the options a, b, c, or d is correct because the profit-maximizing level of output is 1 unit.
1. Understand the data from the table:
- Quantity: [0, 1, 2, 3, 4, 5, 6, 7, 10]
- Price: [[tex]$50, $[/tex]45, [tex]$40, $[/tex]35, [tex]$30, $[/tex]25, [tex]$20, $[/tex]15, [tex]$5] - Marginal Cost: [None, $[/tex]30, [tex]$24, $[/tex]14, [tex]$10, $[/tex]12, [tex]$32, $[/tex]10, [tex]$140] - Average Total Cost: [None, $[/tex]40, [tex]$32, $[/tex]26, [tex]$22, $[/tex]20, [tex]$22, $[/tex]30, [tex]$50] 2. Calculate Total Revenue (TR): - TR = Price * Quantity - TR for Quantity 0: $[/tex]50 * 0 = [tex]$0 TR for Quantity 1: $[/tex]45 * 1 = [tex]$45 TR for Quantity 2: $[/tex]40 * 2 = [tex]$80 TR for Quantity 3: $[/tex]35 * 3 = [tex]$105 TR for Quantity 4: $[/tex]30 * 4 = [tex]$120 TR for Quantity 5: $[/tex]25 * 5 = [tex]$125 TR for Quantity 6: $[/tex]20 * 6 = [tex]$120 TR for Quantity 7: $[/tex]15 * 7 = [tex]$105 TR for Quantity 10: $[/tex]5 * 10 = [tex]$50 3. Calculate Marginal Revenue (MR): - MR is the change in Total Revenue (TR) divided by the change in quantity. MR for Quantity 1: (TR for 1 - TR for 0) / (1 - 0) = ($[/tex]45 - [tex]$0) / 1 = $[/tex]45
MR for Quantity 2: (TR for 2 - TR for 1) / (2 - 1) = ([tex]$80 - $[/tex]45) / 1 = [tex]$35 MR for Quantity 3: (TR for 3 - TR for 2) / (3 - 2) = ($[/tex]105 - [tex]$80) / 1 = $[/tex]25
MR for Quantity 4: (TR for 4 - TR for 3) / (4 - 3) = ([tex]$120 - $[/tex]105) / 1 = [tex]$15 MR for Quantity 5: (TR for 5 - TR for 4) / (5 - 4) = ($[/tex]125 - [tex]$120) / 1 = $[/tex]5
MR for Quantity 6: (TR for 6 - TR for 5) / (6 - 5) = ([tex]$120 - $[/tex]125) / 1 = -[tex]$5 MR for Quantity 7: (TR for 7 - TR for 6) / (7 - 6) = ($[/tex]105 - [tex]$120) / 1 = -$[/tex]15
MR for Quantity 10: (TR for 10 - TR for 7) / (10 - 7) = ([tex]$50 - $[/tex]105) / 3 = -[tex]$18.3 4. Compare Marginal Cost (MC) and Marginal Revenue (MR): - For profit maximization, we find the quantity at which MR = MC: - For Quantity 1: MR = $[/tex]45, MC = [tex]$30 (MR > MC) - For Quantity 2: MR = $[/tex]35, MC = [tex]$24 (MR > MC) - For Quantity 3: MR = $[/tex]25, MC = [tex]$14 (MR > MC) - For Quantity 4: MR = $[/tex]15, MC = [tex]$10 (MR > MC) - For Quantity 5: MR = $[/tex]5, MC = [tex]$12 (MR < MC) At Quantity 1, MR equals $[/tex]45 and MC equals $30. When MR = MC, the firm maximizes its profit. Therefore, the firm's profit-maximizing level of output is:
[tex]\[ \boxed{1 \text{ unit of output}} \][/tex]
Thus, the answer is:
None of the options a, b, c, or d is correct because the profit-maximizing level of output is 1 unit.
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