Question

Consider the cost function C(Q) = 60Q – 12Q² + Q³.

a.   Sketch the total cost, the total variable cost, and the fixed cost for 0-12 units of output.

b.   Find expressions for the ATC, AVC, AFC, and MC curves, and sketch the curves on a single graph, making sure the curves are correctly related to each other. At what output level does ATC reaches its minimum?

c.   What can you say about the shape of the marginal product of labor curve that underlies this cost function? Explain.

Answer 1

C(Q) = 60Q – 12Q2 + Q3

Variable cost is cost of production dependent upon output level produced while fixed cost is independent of Q.

a) Here C(Q) is fully dependent upon Q, thus there is no fixed coxt. The complete cost is variable cost. There is no total variable as well as fixed cost.

Output	Total Cost
0	0
1	49
2	80
3	99
4	112
5	125
6	144
7	175
8	224
9	297
10	400
11	539
12	720

Cost Curves 0 1 2 3 4 5 7 8 9 10 11 12 6 Output - Total Cost

b)

Output	Total Cost	ATC	MC
0	0	-	-
1	49	49	49
2	80	40	31
3	99	33	19
4	112	28	13
5	125	25	13
6	144	24	19
7	175	25	31
8	224	28	49
9	297	33	73
10	400	40	103
11	539	49	139
12	720	60	181

Cost Curves 0 1 2 3 4 5 7 8 9 10 11 12 6 Output Total Cost — ATC -MC

ATC reaches its minimum at output level of 6.

c) Marginal product and marginal cost are inversely related to each other. The portion at which Marginal cost is falling, marginal product rises and vice versa.