Question

A perfectly competitive firm has the following total cost and marginal cost functions:

     TC = 100 + 10q – q² + (1/3)q³

     MC = q² – 2q +10

     a)    For quantities from 0 to 10 determine: TC, TFC, TVC, and MC.

b)    For quantities from 0 to 10 determine: ATC, AFC, and AVC.

c)    Assume P (MR) equals 45. For quantities from 0 to 10 determine: TR and profit.

d)    At what quantity is profit maximized? At this quantity what is true about the relationship between MC and MR?

Answer 1

a., b., c.

Q	TFC	TVC	TC	MC	ATC	AFC	AVC	P	TR	Profit
0.00	100.00	0.00	100.00					45.00	0.00	-100.00
1.00	100.00	9.33	109.33	9.33	109.33	100.00	9.33	45.00	45.00	-64.33
2.00	100.00	18.67	118.67	9.33	59.33	50.00	9.33	45.00	90.00	-28.67
3.00	100.00	30.00	130.00	11.33	43.33	33.33	10.00	45.00	135.00	5.00
4.00	100.00	45.33	145.33	15.33	36.33	25.00	11.33	45.00	180.00	34.67
5.00	100.00	66.67	166.67	21.33	33.33	20.00	13.33	45.00	225.00	58.33
6.00	100.00	96.00	196.00	29.33	32.67	16.67	16.00	45.00	270.00	74.00
7.00	100.00	135.33	235.33	39.33	33.62	14.29	19.33	45.00	315.00	79.67
8.00	100.00	186.67	286.67	51.33	35.83	12.50	23.33	45.00	360.00	73.33
9.00	100.00	252.00	352.00	65.33	39.11	11.11	28.00	45.00	405.00	53.00
10.00	100.00	333.33	433.33	81.33	43.33	10.00	33.33	45.00	450.00	16.67

d.  quantity =7 at profit maximization. At this quantity MC = MR