Question

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)

Answer 1

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