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Sagot :
To answer the given question, we'll tackle each part step-by-step to find the necessary values and understand the firm's financial performance.
### (a) Calculate the values A, B, C, D, E, and F.
1. Calculate [tex]\(A\)[/tex]:
- Given: Total Cost (TC) for 2 units is 16, and Marginal Cost (MC) for the third unit is 7.
- Total Cost for 3 units [tex]\(TC_3\)[/tex] is calculated by adding the Marginal Cost of the third unit to the Total Cost of 2 units.
- Therefore, [tex]\(A = TC_3 = TC_2 + MC_3 = 16 + 7 = 23\)[/tex].
2. Calculate [tex]\(B\)[/tex]:
- Given: Total Cost (TC) for 4 units is 28, and for 6 units is 54. Also, Marginal Cost (MC) for the sixth unit is 16.
- Total Cost for 5 units [tex]\(TC_5\)[/tex] can be calculated by subtracting the Marginal Cost of the sixth unit from the Total Cost of 6 units.
- Therefore, [tex]\(TC_5 = TC_6 - MC_6 = 54 - 16 = 38\)[/tex].
- So, [tex]\(B = TC_5 = 38\)[/tex].
3. Calculate [tex]\(C\)[/tex]:
- Given: Total Cost (TC) for 2 units is 16.
- Average Cost (AC) for 2 units is calculated by dividing the Total Cost by the number of units.
- Therefore, [tex]\(C = AC_2 = \frac{TC_2}{2} = \frac{16}{2} = 8\)[/tex].
4. Calculate [tex]\(D\)[/tex]:
- Given: Total Cost (TC) for 4 units is 28.
- Average Cost (AC) for 4 units is calculated by dividing the Total Cost by the number of units.
- Therefore, [tex]\(D = AC_4 = \frac{TC_4}{4} = \frac{28}{4} = 7\)[/tex].
5. Calculate [tex]\(E\)[/tex]:
- Given: Total Cost (TC) for 3 units is 23 and Total Cost for 2 units is 16.
- Marginal Cost (MC) for the third unit is calculated by subtracting the Total Cost of 2 units from the Total Cost of 3 units.
- Therefore, [tex]\(E = MC_3 = TC_3 - TC_2 = 23 - 16 = 7\)[/tex].
6. Calculate [tex]\(F\)[/tex]:
- Given: Total Cost (TC) for 5 units is 38 and Total Cost for 4 units is 28.
- Marginal Cost (MC) for the fifth unit is calculated by subtracting the Total Cost of 4 units from the Total Cost of 5 units.
- Therefore, [tex]\(F = MC_5 = TC_5 - TC_4 = 38 - 28 = 10\)[/tex].
### Summary of values:
- [tex]\(A = 23\)[/tex]
- [tex]\(B = 38\)[/tex]
- [tex]\(C = 8\)[/tex]
- [tex]\(D = 7\)[/tex]
- [tex]\(E = 7\)[/tex]
- [tex]\(F = 10\)[/tex]
### (b) Firm's Profit Calculation
- Price of product [tex]\(p = \$12\)[/tex].
#### (i) Profit when 2 units are sold:
- Total Revenue (TR) when selling 2 units: [tex]\[ TR = p \times 2 = 12 \times 2 = 24 \][/tex]
- Total Cost (TC) for 2 units: [tex]\[ TC_2 = 16 \][/tex]
- Profit: [tex]\[ \text{Profit} = TR - TC = 24 - 16 = \$8 \][/tex]
#### (ii) Profit when 6 units are sold:
- Total Revenue (TR) when selling 6 units: [tex]\[ TR = p \times 6 = 12 \times 6 = 72 \][/tex]
- Total Cost (TC) for 6 units: [tex]\[ TC_6 = 54 \][/tex]
- Profit: [tex]\[ \text{Profit} = TR - TC = 72 - 54 = \$18 \][/tex]
### (c) Firm's Equilibrium Level
#### (i) Equilibrium Output Level
- A firm is in equilibrium at the output level where Marginal Cost (MC) equals Average Cost (AC).
#### (ii) Reason:
- From the table and calculated values, we see that [tex]\( MC_4 = 7 \)[/tex] and [tex]\( AC_4 = 7 \)[/tex].
- Hence, the firm is in equilibrium at output level 4 units because this is where the MC equals AC.
### Conclusion
With these steps, we have found the necessary values, calculated the firm's profits at different output levels, and determined the equilibrium output level.
### (a) Calculate the values A, B, C, D, E, and F.
1. Calculate [tex]\(A\)[/tex]:
- Given: Total Cost (TC) for 2 units is 16, and Marginal Cost (MC) for the third unit is 7.
- Total Cost for 3 units [tex]\(TC_3\)[/tex] is calculated by adding the Marginal Cost of the third unit to the Total Cost of 2 units.
- Therefore, [tex]\(A = TC_3 = TC_2 + MC_3 = 16 + 7 = 23\)[/tex].
2. Calculate [tex]\(B\)[/tex]:
- Given: Total Cost (TC) for 4 units is 28, and for 6 units is 54. Also, Marginal Cost (MC) for the sixth unit is 16.
- Total Cost for 5 units [tex]\(TC_5\)[/tex] can be calculated by subtracting the Marginal Cost of the sixth unit from the Total Cost of 6 units.
- Therefore, [tex]\(TC_5 = TC_6 - MC_6 = 54 - 16 = 38\)[/tex].
- So, [tex]\(B = TC_5 = 38\)[/tex].
3. Calculate [tex]\(C\)[/tex]:
- Given: Total Cost (TC) for 2 units is 16.
- Average Cost (AC) for 2 units is calculated by dividing the Total Cost by the number of units.
- Therefore, [tex]\(C = AC_2 = \frac{TC_2}{2} = \frac{16}{2} = 8\)[/tex].
4. Calculate [tex]\(D\)[/tex]:
- Given: Total Cost (TC) for 4 units is 28.
- Average Cost (AC) for 4 units is calculated by dividing the Total Cost by the number of units.
- Therefore, [tex]\(D = AC_4 = \frac{TC_4}{4} = \frac{28}{4} = 7\)[/tex].
5. Calculate [tex]\(E\)[/tex]:
- Given: Total Cost (TC) for 3 units is 23 and Total Cost for 2 units is 16.
- Marginal Cost (MC) for the third unit is calculated by subtracting the Total Cost of 2 units from the Total Cost of 3 units.
- Therefore, [tex]\(E = MC_3 = TC_3 - TC_2 = 23 - 16 = 7\)[/tex].
6. Calculate [tex]\(F\)[/tex]:
- Given: Total Cost (TC) for 5 units is 38 and Total Cost for 4 units is 28.
- Marginal Cost (MC) for the fifth unit is calculated by subtracting the Total Cost of 4 units from the Total Cost of 5 units.
- Therefore, [tex]\(F = MC_5 = TC_5 - TC_4 = 38 - 28 = 10\)[/tex].
### Summary of values:
- [tex]\(A = 23\)[/tex]
- [tex]\(B = 38\)[/tex]
- [tex]\(C = 8\)[/tex]
- [tex]\(D = 7\)[/tex]
- [tex]\(E = 7\)[/tex]
- [tex]\(F = 10\)[/tex]
### (b) Firm's Profit Calculation
- Price of product [tex]\(p = \$12\)[/tex].
#### (i) Profit when 2 units are sold:
- Total Revenue (TR) when selling 2 units: [tex]\[ TR = p \times 2 = 12 \times 2 = 24 \][/tex]
- Total Cost (TC) for 2 units: [tex]\[ TC_2 = 16 \][/tex]
- Profit: [tex]\[ \text{Profit} = TR - TC = 24 - 16 = \$8 \][/tex]
#### (ii) Profit when 6 units are sold:
- Total Revenue (TR) when selling 6 units: [tex]\[ TR = p \times 6 = 12 \times 6 = 72 \][/tex]
- Total Cost (TC) for 6 units: [tex]\[ TC_6 = 54 \][/tex]
- Profit: [tex]\[ \text{Profit} = TR - TC = 72 - 54 = \$18 \][/tex]
### (c) Firm's Equilibrium Level
#### (i) Equilibrium Output Level
- A firm is in equilibrium at the output level where Marginal Cost (MC) equals Average Cost (AC).
#### (ii) Reason:
- From the table and calculated values, we see that [tex]\( MC_4 = 7 \)[/tex] and [tex]\( AC_4 = 7 \)[/tex].
- Hence, the firm is in equilibrium at output level 4 units because this is where the MC equals AC.
### Conclusion
With these steps, we have found the necessary values, calculated the firm's profits at different output levels, and determined the equilibrium output level.
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