i can not figure this out

the economist for the grand corporation has estimated the company's cost function, using time series data, to be

a.plot this curve for quantites 1 to 10
b.calculate the average total cost,average variable cost, and marginal cost for these quantities, and plot them on another graph
c. discuss your results in term of decreasing,constant, and increasing marginal costs.


To solve this problem, we need to follow these steps:

Step 1: Plotting the Total Cost Curve
- The given cost function is TC = 50 + 16Q - 2Q^2 + 0.2Q^3.
- To plot the total cost curve, we need to calculate the total cost for different quantities of Q, ranging from 1 to 10.
- Substitute the values of Q into the cost function and calculate the corresponding total costs.
- Plot these points on a graph, with quantities of Q on the x-axis and total costs on the y-axis.

Step 2: Calculating Average Total Cost (ATC)
- Average Total Cost (ATC) is calculated by dividing total cost (TC) by the quantity (Q).
- To find the ATC for each quantity, divide the total cost obtained in Step 1 by the corresponding quantity.
- Plot these ATC values in a separate graph, with quantities of Q on the x-axis and ATC on the y-axis.

Step 3: Calculating Average Variable Cost (AVC)
- Average Variable Cost (AVC) is calculated by dividing variable cost (VC) by the quantity (Q).
- Variable cost is the part of the total cost that varies with the quantity produced.
- To find the AVC for each quantity, exclude the fixed cost component (50) from the total cost obtained in Step 1 and divide by the corresponding quantity.
- Plot these AVC values in the same graph used for ATC.

Step 4: Calculating Marginal Cost (MC)
- Marginal Cost (MC) is calculated as the change in total cost divided by the change in quantity (∆TC / ∆Q).
- To find the MC for each quantity, calculate the difference in total costs between successive quantities and divide by the difference in quantities.
- Plot these MC values on the second graph used for ATC and AVC.

Step 5: Analyzing Results
- Examine the plot of MC values obtained in Step 4.
- If MC is decreasing, it indicates economies of scale, meaning the cost per unit decreases as quantity increases.
- If MC is constant, it suggests constant returns to scale, indicating that the cost per unit remains the same regardless of the quantity.
- If MC is increasing, it implies diseconomies of scale, where the cost per unit increases with higher quantities.

By following these steps, you can plot the cost curve and analyze the average total cost, average variable cost, and marginal cost to interpret the company's cost behavior.