Question

A competitive firm's cost of producing q units of output is C = 18 + 4q + q^2 Its corresponding marginal cost is MC = 4 + 2q. a. The firm faces a market price p = $24. Create a spreadsheet with q = 0, 1, 2, ..... 15, where the columns are q, R, C, VC, AVC, MC, and profit. Determine the profit-maximizing output for the firm and the corresponding profit. Should the firm produce this level of output or should it shut down? Explain. b. Suppose the competitive price declines to p = $12. Repeat the calculations of part a. Should the firm shut down? Please show Excel formulas. Thanks!

Answer 1

(a)

R = p x q = $24 x q

C = 18 + 4q + q²

VC = 4q + q²

AVC = VC/q = 4 + q

MC = dC/dq = 4 + 2q

Profit = R - C

q	R	C	VC	AVC	MC	Profit
0	0	18	0			-18
1	24	23	5	5	5	1
2	48	30	12	6	7	18
3	72	39	21	7	9	33
4	96	50	32	8	11	46
5	120	63	45	9	13	57
6	144	78	60	10	15	66
7	168	95	77	11	17	73
8	192	114	96	12	19	78
9	216	135	117	13	21	81
10	240	158	140	14	23	82
11	264	183	165	15	25	81
12	288	210	192	16	27	78
13	312	239	221	17	29	73
14	336	270	252	18	31	66
15	360	303	285	19	33	57

Profit is maximized (= $82) when q = 10 units. At this output, AVC < Price ($14 < $24), so firm should continue to operate.

(b)

Price = $12
q	R	C	VC	AVC	MC	Profit
0	0	18	0			-18
1	12	23	5	5	5	-11
2	24	30	12	6	7	-6
3	36	39	21	7	9	-3
4	48	50	32	8	11	-2
5	60	63	45	9	13	-3
6	72	78	60	10	15	-6
7	84	95	77	11	17	-11
8	96	114	96	12	19	-18
9	108	135	117	13	21	-27
10	120	158	140	14	23	-38
11	132	183	165	15	25	-51
12	144	210	192	16	27	-66
13	156	239	221	17	29	-83
14	168	270	252	18	31	-102
15	180	303	285	19	33	-123

In this case firm is making loss at every output level, and loss is minimized (= -$2) when q = 4 units. At this output, AVC < Price ($8 < $12), so firm should not shut down.

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