Understanding Fixed and Marginal Cost in Polynomial Total Cost Functions
Total Cost in Economics: In economics, the total cost (CQ) of producing a certain quantity (Q) of goods is the sum of fixed cost (FC) and variable cost (VC). The fixed cost remains constant regardless of the quantity produced, while the variable cost changes with the quantity.
Given Total Cost Function
The problem presented is a polynomial total cost function given by:
CQ 3Q2 - 4Q 5
Fixed Cost (FC)
Fixed Cost is the part of the total cost that remains constant and does not change with the level of production.
Given total cost function: CQ 3Q2 - 4Q 5
The fixed cost is the constant term in the equation. It is the cost when no goods are produced (Q 0).
Fixed Cost (FC): 5
Marginal Cost (MC)
Marginal Cost (MC) is the additional cost incurred when producing one more unit of output. It is the derivative of the total cost function with respect to Q.
Calculating Marginal Cost
To find the marginal cost, we need to differentiate the total cost function with respect to Q.
Total cost function: CQ 3Q2 - 4Q 5
Marginal cost (MC):
Marginal Cost (MC) dCQ/dQ d/dQ (3Q2 - 4Q 5) 6Q - 4
Summary
Fixed Cost: 5
Marginal Cost: 6Q - 4
The marginal cost varies with the quantity produced, as shown by the formula 6Q - 4. This reflects the idea that the additional cost of producing an extra unit of output increases as more units are produced.
Additional Insights
Fixed Cost Interpretation: Fixed cost is the minimum total cost when no goods are produced, or it is simply the cost term that does not involve Q. In this case, it is a constant 5, meaning it remains unchanged regardless of production levels.
Marginal Cost Observations: The marginal cost function 6Q - 4 indicates an increasing marginal cost since the coefficient of Q (6) is positive. This suggests that producing additional units beyond a certain point becomes more expensive.
Conclusion
In the polynomial total cost function CQ 3Q2 - 4Q 5, the fixed cost is 5 and the marginal cost is 6Q - 4. Understanding these concepts is crucial for assessing the economic efficiency of production levels.