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Sagot :
Sure, let's tackle the problem step-by-step.
### (a) Calculate the values A, B, C, D, E, and F.
1. Calculate C (Average Cost at Output = 2):
- AC = TC / Output.
- Given: TC for Output = 2 is 16.
- Output = 2 units.
- [tex]\( C = \frac{16}{2} = 8 \)[/tex].
2. Calculate A (Total Cost at Output = 3):
- AC (Average Cost) for Output = 3 is given as 7.
- Output = 3 units.
- [tex]\( A = AC \times \text{Output} = 7 \times 3 = 21 \)[/tex].
3. Calculate E (Marginal Cost between Output = 2 and Output = 3):
- MC = Change in TC / Change in Output.
- Change in Output = Output(3) - Output(2) = 3 - 2 = 1 unit.
- Change in TC = TC(3) - TC(2) = 21 - 16 = 5.
- [tex]\( E = \frac{5}{1} = 5 \)[/tex].
4. Calculate D (Average Cost at Output = 4):
- TC for Output = 4 is given as 28.
- Output = 4 units.
- [tex]\( D = \frac{28}{4} = 7 \)[/tex].
5. Calculate B (Total Cost at Output = 5):
- AC (Average Cost) for Output = 5 is given as 8.
- Output = 5 units.
- [tex]\( B = AC \times \text{Output} = 8 \times 5 = 40 \)[/tex].
6. Calculate F (Marginal Cost between Output = 5 and Output = 6):
- MC = Change in TC / Change in Output.
- Change in Output = Output(6) - Output(5) = 6 - 5 = 1 unit.
- Change in TC = TC(6) - TC(5) = 54 - 40 = 14.
- [tex]\( F = \frac{14}{1} = 14 \)[/tex].
So, the calculated values are:
- [tex]\( A = 21 \)[/tex]
- [tex]\( B = 40 \)[/tex]
- [tex]\( C = 8 \)[/tex]
- [tex]\( D = 7 \)[/tex]
- [tex]\( E = 5 \)[/tex]
- [tex]\( F = 14 \)[/tex]
### (b) Calculate the firm's profit when:
(i) 2 units are sold:
- Price per unit = \[tex]$12. - Output = 2 units. - Revenue = Price × Output \( = 12 \times 2 = 24 \). - TC for Output = 2 is given as 16. - Profit = Revenue - TC \( = 24 - 16 = 8 \). (ii) 6 units are sold: - Price per unit = \$[/tex]12.
- Output = 6 units.
- Revenue = Price × Output [tex]\( = 12 \times 6 = 72 \)[/tex].
- TC for Output = 6 is given as 54.
- Profit = Revenue - TC [tex]\( = 72 - 54 = 18 \)[/tex].
So, the profits are:
- For 2 units: \[tex]$8. - For 6 units: \$[/tex]18.
### (c) (i) At what output level is the firm in equilibrium?
The firm is in equilibrium when Marginal Cost (MC) equals the price of the firm's product. Given that the price is \[tex]$12: - Looking at the marginal costs, we see that none of the given marginal costs (9, 7, 5, 7, 14) are equal to 12. - Therefore, there is no output level where the firm is in equilibrium, given the provided data. (ii) Give a reason for your answer in (c) (i) above. - The firm is in equilibrium when the Marginal Cost (MC) is equal to the price of the product. Since none of the MCs provided match the given price of \$[/tex]12, there is no output level where the firm is in equilibrium.
### (a) Calculate the values A, B, C, D, E, and F.
1. Calculate C (Average Cost at Output = 2):
- AC = TC / Output.
- Given: TC for Output = 2 is 16.
- Output = 2 units.
- [tex]\( C = \frac{16}{2} = 8 \)[/tex].
2. Calculate A (Total Cost at Output = 3):
- AC (Average Cost) for Output = 3 is given as 7.
- Output = 3 units.
- [tex]\( A = AC \times \text{Output} = 7 \times 3 = 21 \)[/tex].
3. Calculate E (Marginal Cost between Output = 2 and Output = 3):
- MC = Change in TC / Change in Output.
- Change in Output = Output(3) - Output(2) = 3 - 2 = 1 unit.
- Change in TC = TC(3) - TC(2) = 21 - 16 = 5.
- [tex]\( E = \frac{5}{1} = 5 \)[/tex].
4. Calculate D (Average Cost at Output = 4):
- TC for Output = 4 is given as 28.
- Output = 4 units.
- [tex]\( D = \frac{28}{4} = 7 \)[/tex].
5. Calculate B (Total Cost at Output = 5):
- AC (Average Cost) for Output = 5 is given as 8.
- Output = 5 units.
- [tex]\( B = AC \times \text{Output} = 8 \times 5 = 40 \)[/tex].
6. Calculate F (Marginal Cost between Output = 5 and Output = 6):
- MC = Change in TC / Change in Output.
- Change in Output = Output(6) - Output(5) = 6 - 5 = 1 unit.
- Change in TC = TC(6) - TC(5) = 54 - 40 = 14.
- [tex]\( F = \frac{14}{1} = 14 \)[/tex].
So, the calculated values are:
- [tex]\( A = 21 \)[/tex]
- [tex]\( B = 40 \)[/tex]
- [tex]\( C = 8 \)[/tex]
- [tex]\( D = 7 \)[/tex]
- [tex]\( E = 5 \)[/tex]
- [tex]\( F = 14 \)[/tex]
### (b) Calculate the firm's profit when:
(i) 2 units are sold:
- Price per unit = \[tex]$12. - Output = 2 units. - Revenue = Price × Output \( = 12 \times 2 = 24 \). - TC for Output = 2 is given as 16. - Profit = Revenue - TC \( = 24 - 16 = 8 \). (ii) 6 units are sold: - Price per unit = \$[/tex]12.
- Output = 6 units.
- Revenue = Price × Output [tex]\( = 12 \times 6 = 72 \)[/tex].
- TC for Output = 6 is given as 54.
- Profit = Revenue - TC [tex]\( = 72 - 54 = 18 \)[/tex].
So, the profits are:
- For 2 units: \[tex]$8. - For 6 units: \$[/tex]18.
### (c) (i) At what output level is the firm in equilibrium?
The firm is in equilibrium when Marginal Cost (MC) equals the price of the firm's product. Given that the price is \[tex]$12: - Looking at the marginal costs, we see that none of the given marginal costs (9, 7, 5, 7, 14) are equal to 12. - Therefore, there is no output level where the firm is in equilibrium, given the provided data. (ii) Give a reason for your answer in (c) (i) above. - The firm is in equilibrium when the Marginal Cost (MC) is equal to the price of the product. Since none of the MCs provided match the given price of \$[/tex]12, there is no output level where the firm is in equilibrium.
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