Question

You are given the following total cost function for a firm:

           TC = (25+F) + L x Q + 0.5 x (Q²)

where F=the number of the letter of the alphabet corresponding to the initial of your first name, and L=number of the letter of the alphabet corresponding to the initial of your last name.  For example, if your name were Bill Weber, F=2 and L=23, so

TC = 27 + 23 x Q + 0.5 x Q².

a.         Calculate TC, TFC, and TVC for the levels of output between Q=0 and Q=30 (i.e.,  Q=0, Q=1, Q=2, Q=3,..., Q=29, Q=30).  Make a graph of TC, TFC, and TVC as a function of Q.  (Use an xy graph, connect the points, and make sure these three curves are all on the same graph.)  

Answer 1

TC = 27 + 23Q + 0.5Q2

TFC = 27.

Note: TFC is the constant part of TC.

TVC = 23Q + 0.5Q2

Note: TVC is the that part of TC which depends on Q

Q	TC	TFC	TVC
0	27	27	0
1	50.5	27	23.5
2	75	27	48
3	100.5	27	73.5
4	127	27	100
5	154.5	27	127.5
6	183	27	156
7	212.5	27	185.5
8	243	27	216
9	274.5	27	247.5
10	307	27	280
11	340.5	27	313.5
12	375	27	348
13	410.5	27	383.5
14	447	27	420
15	484.5	27	457.5
16	523	27	496
17	562.5	27	535.5
18	603	27	576
19	644.5	27	617.5
20	687	27	660
21	730.5	27	703.5
22	775	27	748
23	820.5	27	793.5
24	867	27	840
25	914.5	27	887.5
26	963	27	936
27	1012.5	27	985.5
28	1063	27	1036
29	1114.5	27	1087.5
30	1167	27	1140