Suppose an electricity generating firm exists with the following cost functions, C(Q) = 2Q^2 + 3Q + 72, FC = 72, MC(Q) = 4Q + 3, AC(Q) = 2Q + 3 + (72/Q), AVC(Q) = 2Q + 3
Graph the AC(Q), the AVC(Q), the MC(Q) on the same graph below. Hint, this is easiest to do by creating a schedule with quantity from 1 – 10 and calculating the corresponding costs for each quantity. I.e., when Q = 1, the AVC =? MC=? AC=? (6 pts)
Now using the char from above, how much profit does the firm receive at a price of $27?
Now using the charts and equations from above, how much profit does the firm receive at a price of $39? Hint: Show your work and find the quantity sold and calculate the revenues and costs. (3 pts)
The graph representing the above equation of cost
AC(Q), the AVC(Q), MC(Q)
Quantity | TC | AC | AVC | MC |
1 | 77 | 77 | 5 | 7 |
2 | 86 | 43 | 7 | 9 |
3 | 99 | 33 | 9 | 13 |
4 | 116 | 29 | 11 | 17 |
5 | 137 | 27.4 | 13 | 21 |
6 | 162 | 27 | 15 | 25 |
7 | 191 | 27.28571429 | 17 | 29 |
8 | 224 | 28 | 19 | 33 |
9 | 261 | 29 | 21 | 37 |
10 | 302 | 30.2 | 23 | 41 |
11 | 347 | 31.54545455 | 25 | 45 |
12 | 396 | 33 | 27 | 49 |
13 | 449 | 34.53846154 | 29 | 53 |
14 | 506 | 36.14285714 | 31 | 57 |
15 | 567 | 37.8 | 33 | 61 |
16 | 632 | 39.5 | 35 | 65 |
17 | 701 | 41.23529412 | 37 | 69 |
18 | 774 | 43 | 39 | 73 |
19 | 851 | 44.78947368 | 41 | 77 |
20 | 932 | 46.6 | 43 | 81 |
WHEN PRICE IS $27
profit = Total Revenue - Tota Cost
Total Revenue(TR) = Price*Quantity
TR = 27Q
TC = 2Q^2+ 3Q +72
PROFIT = 27Q - 2Q^2 - 3Q - 72
PROFIT = 24Q - 2Q^2 - 72
First order difffential
d(profit)/d(Q) = 24 - 4Q
PUT ABOVE EQUATION EUALT TO 0 (ZERO)
24 - 4Q = 0
4Q=24
Q=24/4 = 6
QUANTITY SOLD IS 6
TOTAL REVENUE = 27Q = 27*6 = 162
TOTAL COST = 162 (from above table)
Profit = $ 0
WHEN PRICE IS $ 39
profit = Total Revenue - Tota Cost
Total Revenue(TR) = Price*Quantity
TR = 39Q
TC = 2Q^2+ 3Q +72
PROFIT = 39Q - 2Q^2 - 3Q - 72
PROFIT = 36Q - 2Q^2 - 72
First order difffential
d(profit)/d(Q) = 36 - 4Q
PUT ABOVE EQUATION EUALT TO 0 (ZERO)
36 - 4Q = 0
4Q=36
Q=36/4 = 9
QUANTITY SOLD IS 9
TOTAL REVENUE = 39Q = 39*6 = 351
TOTAL COST = 261 (from above table)
Profit = $ 90
Suppose an electricity generating firm exists with the following cost functions, C(Q) = 2Q^2 + 3Q...
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