Question

Suppose that the cost function of some manufacturer is TC(q) = 160 + 8q + 10q^2 .

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

2. Sketch the ATC, AVC, and MC curves. At what output level does the firm’s ATC

   reach its minimum point?

3. 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 = 160 + 8q + 10q^² ............ (1)

ATC = TC / q = (160 / q) + 8 + 10q ................ (2)

VC (dependent on "q") = 8q + 10q^²

AVC = VC / q = 8 + 10q............... (3)

FC (independent of "q") = 160

AFC = FC / q = 160 / q ............. (4)

MC (first derivative of TC with respect to q) = 8 + 20q ............. (5)

Output	TC	VC	FC	ATC	AVC	AFC	MC
0	160	0	160	-	-	-	-
1	178	18	160	178.00	18.00	160.00	18
2	216	56	160	108.00	28.00	80.00	38
3	274	114	160	91.33	38.00	53.33	58
4	352	192	160	88.00	48.00	40.00	78
5	450	290	160	90.00	58.00	32.00	98
6	568	408	160	94.67	68.00	26.67	118
7	706	546	160	100.86	78.00	22.86	138
8	864	704	160	108.00	88.00	20.00	158
9	1042	882	160	115.78	98.00	17.78	178
10	1240	1080	160	124.00	108.00	16.00	198

ATC is at its minimum when 4 units is produced.

When MC as well we AVC is rising, MP and AP is falling. As MC > AVC, MP would be less than AP.