Question
Suppose a cost function is given as . C= 0.05Q^2+.0.1Q+20
Determine:
A. TFC
. TVC and ATC of producing 6 units
. MC of the 6th unit
Determine:
A. TFC
. TVC and ATC of producing 6 units
. MC of the 6th unit
Answers
GPT 3.5
To determine the Total Fixed Cost (TFC), we need to identify the component of the cost function that represents fixed costs.
In the given cost function, C = 0.05Q^2 + 0.1Q + 20, the constant term 20 represents the fixed costs. Therefore, TFC = $20.
To determine the Total Variable Cost (TVC), we can subtract the fixed cost from the total cost:
TVC = C - TFC = 0.05Q^2 + 0.1Q + 20 - 20 = 0.05Q^2 + 0.1Q.
To find the Average Total Cost (ATC) of producing 6 units, we divide the total cost by the quantity:
ATC = C/Q = (0.05Q^2 + 0.1Q + 20)/Q = 0.05Q + 0.1 + 20/Q.
Substituting Q = 6, we find:
ATC(6) = 0.05(6) + 0.1 + 20/6 = 0.3 + 0.1 + 20/6 ≈ 0.5 + 3.333 ≈ 3.833.
To find the Marginal Cost (MC) of the 6th unit, we take the derivative of the cost function with respect to quantity (Q) and evaluate it at Q = 6:
MC = dC/dQ = 0.1Q + 0.1.
Substituting Q = 6, we find:
MC(6) = 0.1(6) + 0.1 = 0.6 + 0.1 = 0.7.
In the given cost function, C = 0.05Q^2 + 0.1Q + 20, the constant term 20 represents the fixed costs. Therefore, TFC = $20.
To determine the Total Variable Cost (TVC), we can subtract the fixed cost from the total cost:
TVC = C - TFC = 0.05Q^2 + 0.1Q + 20 - 20 = 0.05Q^2 + 0.1Q.
To find the Average Total Cost (ATC) of producing 6 units, we divide the total cost by the quantity:
ATC = C/Q = (0.05Q^2 + 0.1Q + 20)/Q = 0.05Q + 0.1 + 20/Q.
Substituting Q = 6, we find:
ATC(6) = 0.05(6) + 0.1 + 20/6 = 0.3 + 0.1 + 20/6 ≈ 0.5 + 3.333 ≈ 3.833.
To find the Marginal Cost (MC) of the 6th unit, we take the derivative of the cost function with respect to quantity (Q) and evaluate it at Q = 6:
MC = dC/dQ = 0.1Q + 0.1.
Substituting Q = 6, we find:
MC(6) = 0.1(6) + 0.1 = 0.6 + 0.1 = 0.7.