To find TFC (total fixed cost), we need to analyze the given cost function. In this case, TFC refers to the fixed costs that do not vary with the level of output. From the given cost function C = Q^3 - 3Q^2 + 8Q + 48, we can deduce that the fixed costs are represented by the constant term, which is 48. Therefore, TFC = 48.
To find TVC (total variable cost), we need to exclude the fixed costs from the total cost function. In this case, TVC refers to the variable costs that do vary with the level of output. From the given cost function C = Q^3 - 3Q^2 + 8Q + 48, we can deduce that TVC is the rest of the cost function excluding the constant term. Therefore, TVC = Q^3 - 3Q^2 + 8Q.
To find AFC (average fixed cost), we divide TFC by the level of output (Q). In this case, AFC = TFC / Q. Since TFC = 48, AFC = 48 / Q.
To find AVC (average variable cost), we divide TVC by the level of output (Q). In this case, AVC = TVC / Q. Since TVC = Q^3 - 3Q^2 + 8Q, AVC = (Q^3 - 3Q^2 + 8Q) / Q = Q^2 - 3Q + 8.
To find AC (average cost), we divide the total cost (C) by the level of output (Q). In this case, AC = C / Q = (Q^3 - 3Q^2 + 8Q + 48) / Q = Q^2 - 3Q + 8 + (48 / Q).
To find MC (marginal cost), we take the derivative of the total cost function with respect to the level of output (Q). In this case, MC = dC / dQ = 3Q^2 - 6Q + 8.
To find the minimum point of MC, we need to set its derivative equal to zero and solve for Q.
3Q^2 - 6Q + 8 = 0
Using the quadratic formula, we can find the roots:
Q = (6 ± sqrt((-6)^2 - 4(3)(8))) / (2(3))
Q = (6 ± sqrt(36 - 96)) / 6
Q = (6 ± sqrt(-60)) / 6
Since the square root of a negative number is not a real number, there are no real solutions for Q in this case. Thus, there is no minimum point of MC.
To find the minimum point of AVC, we need to set its derivative equal to zero and solve for Q.
Q^2 - 3Q + 8 = 0
Using the quadratic formula, we can find the roots:
Q = (3 ± sqrt((-3)^2 - 4(1)(8))) / (2(1))
Q = (3 ± sqrt(9 - 32)) / 2
Q = (3 ± sqrt(-23)) / 2
Since the square root of a negative number is not a real number, there are no real solutions for Q in this case. Thus, there is no minimum point of AVC.
To determine the level of output for which MC = AVC, we need to set the two equations equal to each other and solve for Q.
3Q^2 - 6Q + 8 = Q^2 - 3Q + 8
2Q^2 = 0
Q^2 = 0
Q = 0
Therefore, the level of output for which MC = AVC is 0.
Given a total cost function: C= Q3 - 3Q2 + 8Q + 48 ,then find,
TFC, TVC ,
AFC,AVC, AC and MC
the minimum point of MC and the minimum point of AVC
Determine the level of output for which MC=AVC.
1 answer
1 answer