How do you generate the average variable function (AVC) given the estimated marginal cost function (SMC)?
I got a few answers but I don't know which one is correct.
If the SMC = 80 - 0.1Q + 0.0001Q2, what would be the correct answer fo AVC?
I'm still a bit confused.
Total cost can be derived by integrating the marginal cost function.
I get TC = 9=80Q - (.1/2)Q^2 + (.0001/3)Q^3.
Devide by Q to get AVC
To generate the average variable cost function (AVC) given the estimated marginal cost function (SMC), you need to understand the relationship between these two cost functions. The average variable cost (AVC) is calculated by dividing the total variable cost (TVC) by the quantity of output produced.
Here's the step-by-step process to generate the AVC function using the SMC function:
1. Determine the relationship between SMC and AVC:
- The marginal cost (SMC) is the additional cost incurred from producing one extra unit of output.
- The average variable cost (AVC) is the variable cost per unit of output.
2. Use the relationship between SMC and AVC to determine the formula:
- The AVC can be expressed as AVC = TVC / Q, where AVC is the average variable cost, TVC is the total variable cost, and Q is the quantity of output produced.
- The TVC can be found by integrating the SMC function over the range of quantities.
3. Integrate the SMC function to obtain the TVC function:
- To integrate the SMC function, you need to know the explicit functional form of the SMC equation.
- If you have the explicit functional form, you can integrate it using calculus techniques.
- If you only have a set of data points representing the SMC function, you can use numerical integration methods to estimate the TVC function.
4. Divide the TVC function by the quantity of output (Q) to find the AVC function:
- Once you have the TVC function, divide it by the quantity of output (Q) to obtain the AVC function.
- The resulting AVC function will give you the average variable cost per unit of output.
Keep in mind that the accuracy of the AVC function depends on the accuracy of the SMC function and the integration method used. It's important to have reliable data or a well-defined functional form for the SMC function to obtain a meaningful AVC function.