Q.(a) If the total cost = 10 + Q^3, find AC, AVC, TFC, AFC when Q = 5.
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Start your 14-day free trial to unlock the full solution →(a) From TC = 10 + Q^3 at Q = 5: TFC = 10, AFC = 2, AVC = 25 and AC = 27. (b) By Cramer's rule the solution of x + 3y = 1 and 3x - 2y = 14 is x = 4, y = -1.
(a) Cost measures from TC = 10 + Q^3 at Q = 5.
In the total cost function TC = 10 + Q^3, the constant term (10) does not change with output, so it is the fixed cost, while the Q^3 term varies with output.
- Total Fixed Cost: TFC = 10 (the constant, independent of Q).
- Total Variable Cost: TVC = Q^3 = 5^3 = 125.
- Total Cost: TC = 10 + 125 = 135.
Now the averages at Q = 5:
- Average Cost: AC = TC / Q = 135 / 5 = 27.
- Average Variable Cost: AVC = TVC / Q = 125 / 5 = 25.
- Average Fixed Cost: AFC = TFC / Q = 10 / 5 = 2.
(Check: AC = AVC + AFC = 25 + 2 = 27, which is correct.)
(b) Solving by Cramer's rule: x + 3y = 1 and 3x - 2y = 14.
Write the coefficients. The coefficient determinant D uses the coefficients of x and y:
D = (1)(-2) - (3)(3) = -2 - 9 = -11.
For Dx, replace the x-column with the constants (1, 14):
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