Question

Suppose that the cost function of some manufacturer is TC(q) = 160 + 8q + 10q2 .

a. Find expressions for the firm’s ATC, AVC, AFC, and MC curves.

b. Sketch the ATC, AVC, and MC curves. At what output level does the firm’s ATC reach its minimum point?

c. What can you say about the marginal product curve (for the variable factor; e.g., MPL) that must underlie this cost function? Briefly explain.

Answer 1

TC (q) = 160 + 8q + 10q^²

a)

• ATC = (TC / q) = (160 / q) + 8 + 10q
• Variable Cost is the portion of total cost which is dependent on q. Thus variable cost is 8q + 10q^². AVC = (Variable cost / q) = (8 + 10q)
• Fixed Cost is the portion of total cost which is independent on q. Thus variable cost is 160. AFC = (Fixed cost / q) = (160 / q)
• MC = First derivative of total cost function with respect to q = 8 + 20q

b)

Output	Total Cost	VC	FC	AVC	AFC	MC	ATC
0	160	0	160	-	-	-	-
1	178	18	160	18	160.0	18	178.00
2	216	56	160	28	80.0	38	108.00
3	274	114	160	38	53.3	58	91.33
4	352	192	160	48	40.0	78	88.00
5	450	290	160	58	32.0	98	90.00
6	568	408	160	68	26.7	118	94.67
7	706	546	160	78	22.9	138	100.86
8	864	704	160	88	20.0	158	108.00
9	1042	882	160	98	17.8	178	115.78
10	1240	1080	160	108	16.0	198	124.00

ATC reach its minimum when output level is 4.

c) As MC is rising from 0 to 10, marginal product must be falling along that portion which can be observed after observing the relation below.