if C is give as 5Q^2+ 8Q+20
find the
tota cost,
fixid cost,
marginal cost,
and variable cost
is the firm with the above cost function in the short-run or long-run?
To find the total cost, fixed cost, marginal cost, variable cost, and determine whether the firm is in the short-run or long-run, we need to analyze the given cost function.
The cost function provided is:
C = 5Q^2 + 8Q + 20
1. Total Cost:
Total Cost (TC) refers to the sum of fixed costs (FC) and variable costs (VC). From the given cost function, we can determine that fixed costs (FC) are the constant term in the equation, which is 20 in this case. Variable costs (VC) are the terms dependent on the quantity (Q). In this equation, both the quadratic term (5Q^2) and the linear term (8Q) are dependent on Q. Therefore, the total cost is the complete equation:
TC = 5Q^2 + 8Q + 20
2. Fixed Cost:
Fixed costs (FC) are costs that do not vary with the quantity produced. In the given cost function, the fixed cost is the constant term, which is 20. Hence, the fixed cost is 20.
3. Marginal Cost:
Marginal Cost (MC) refers to the change in total cost resulting from the production of an additional unit. It is the derivative of the total cost function with respect to quantity (Q). To find the marginal cost, we need to differentiate the total cost equation with respect to Q:
MC = dC/dQ
Taking the derivative of the given cost function, we get:
MC = dC/dQ = 10Q + 8
Therefore, the marginal cost is 10Q + 8.
4. Variable Cost:
Variable costs (VC) are costs that vary with the quantity produced. In the given cost function, the variable cost is the sum of the terms that depend on Q:
VC = 5Q^2 + 8Q
Hence, the variable cost is 5Q^2 + 8Q.
5. Determining Short-run or Long-run:
The distinction between the short-run and the long-run depends on the context of the question and the specifics of the problem. The given cost function does not provide any information to determine whether the firm is in the short-run or long-run. Additional information or context specific to the problem is needed to answer this question accurately.
In summary:
- Total Cost (TC) = 5Q^2 + 8Q + 20
- Fixed Cost (FC) = 20
- Marginal Cost (MC) = 10Q + 8
- Variable Cost (VC) = 5Q^2 + 8Q
Note: Please provide further details or context if available to determine whether the firm is in the short-run or long-run.