Question

Firm B’s short-run cost function is:

C = 12 - 2q + 3q2 + F Find the following: A. AFC B. AVC C. ATC D. MC E. At what output quantity is average total cost (ATC) minimized? Assume F = 63. F. At what output quantity does the MC curve cross the ATC and AVC curves? Assume F = 63 G. Graph the AFC, AVC, ATC and MC curves. Assume F = 63.

Answer 1

C = 12 - 2q + 3q^² + F

Total Cost = Fixed Cost + Variable Cost

Cost which is not dependent on output level is fixed cost. In the above function, 12 + F is independent of output and thus a fixed cost.

Variable cost = -2q + 3q^²

A) AFC = Fixed Cost / Output

AFC = [(12 + F) / q]

B) AVC = VC / q

AVC = -2 + 3q

C) ATC = C / q

ATC = (12 / q) - 2 + 3q + (F / q)

D) MC = First Derivative of TC with respect to q = -2 + 6q

E) ATC is minimized when first derivative of ATC with respect to q equals zero

Minimum ATC occurs when = -(12 / q^²) + 3 - (F / q^²) where F = 63

q = 5

F) MC equals ATC when -2 + 6q = (12 / q) - 2 + 3q + (F / q) where F = 63

q = 5

MC equals AVC when AVC is at its minimum which occurs at output level 1.

G)

Quantity	Cost	FC	VC	MC	ATC	AVC	AFC
0	75	75	0	-	-	-	-
1	76	75	1	1	76.00	1	75.00
2	83	75	8	7	41.50	4	37.50
3	96	75	21	13	32.00	7	25.00
4	115	75	40	19	28.75	10	18.75
5	140	75	65	25	28.00	13	15.00
6	171	75	96	31	28.50	16	12.50
7	208	75	133	37	29.71	19	10.71
8	251	75	176	43	31.38	22	9.38