6. A computer virus has attacked a local company's accounting system, leaving many files badly damaged. The following table is all that is left of a file summarizing the firm's cost structure.Unfortunately, much of the data is missing!

Quantity Produced Total Cost Total Variable Cost Average Variable Cost Average Fixed Cost Marginal Cost

0 500 N/A N/A N/A N/A

1 546,1 46,1 46.1 500,0 46.1

2 584,8 84,8 42,4 250,0 38,7

3 616,7 116,7 38,9 166,7 31,9

4 642,4 142,4 35,6 125.0 25,7

5 662,5 162,5 32,5 100,0 20,1

6 677,6 177,6 29,6 83,3 15,1

7 688,3 188,3 26,9 71,4 10,7

(Note that the "marginal cost" column represents the incremental cost of increasing output to the level given in that row. E.g., the 10.7 in the row for Q = 7

(a) Use your knowledge of cost functions to fill in all the blanks in the table.

(b) Some of your colleagues have been playing with the data in the table and claim they have found a formula that summarizes the total costs in the table in a single function. At a meeting you are presented with three options:

Option 1:TC = 500 + 50Q - 4Q²+ 0.1Q³

Option 2:TC = 501 + 47.25Q - 2.95Q²

Option 3:TC = 500 + 49.8Q - 3.7Q²

Which total cost function seems more correct? (I.e., which one best matches the data in the table?)

(c) Why might it be useful to be able to express total cost as a general function of Q rather than just having the table above?

(d) Using the correct total cost formula from the previous question, derive and write down the following four formulas as a function of Q:

Total Variable Cost =

Average Variable Cost =

Average Fixed Cost =

Marginal Cost =

(Hint: Except for marginal cost, you should be check your solutions by using your derived formulas to check the numbers in the table. Marginal cost won't check since in the table we calculated MC as the discrete change in total cost so it will yield slightly different results.)

(e) Using your answers to the previous part, when is MC=AVC?