Question

Second Look Enterprises (SLE) buys old computers, fixes them up, and resells them. Its weekly revenue function is R = 404 - 2q2, so its marginal revenue is MR = 40 - 4. Its weekly cost function is C=10q+0.592, so its marginal cost is MC = 10+q. + 40 a + -2 g² 0.5 g? -49 q 10 a 40 MR + 0 000 MC + 10 a) Calculate SLE's revenue, cost, and profit for q = 1 to q = 20 in increments of 1. SLE's manager wants to maximize profit. Calculate MR and MC for q = 1 to 9 = 20 in increments of 1 and erify that MR = MC at the profit-maximizing output level. Profit MC MR $36 $32 $38 $72 $1021 $128 $150 $168 $1821 $1921 $1981 $200 $198 $192 $182 $168 $150 $128 $11 $22 S35 $48 $63 $78 $95 $112 $131 $150 $171 s192 $215 $238 $263 $288 $315 $342 $371 $400 S25 -S $26 $102 S27 $72 $28 -$32 -$36 -$40 | $38 $o S29 20 S30 Determine the level of output at which the profit is maximized. The maximum profit is when the output is b) Now assume that SLE is run by a manager who is paid 10% of the revenue and therefore wants to maximize revenue. Determine the level of output and marginal revenue at which the revenue is maximized. The maximum revenue is when the output is and the marginal revenue c) Now suppose that SLE is acquired and managed by a philanthropist who wants to promote recycling of used computers and therefore produces as much output as possible as long as the firm does not make losses. Determine the level of output at which the firm makes no losses. The maximum output the firm can produce to not make losses is

Answer 1

a) Profit is defined as the difference between revenue and cost.

q	R	C	Profit	MR	MC
1	38	11	28	36	11
2	72	22	50	32	12
3	102	35	68	28	13
4	128	48	80	24	14
5	150	63	88	20	15
6	168	78	90	16	16
7	182	95	88	12	17
8	192	112	80	8	18
9	198	131	68	4	19
10	200	150	50	0	20
11	198	171	28	-4	21
12	192	192	0	-8	22
13	182	215	-33	-12	23
14	168	238	-70	-16	24
15	150	263	-113	-20	25
16	128	288	-160	-24	26
17	102	315	-213	-28	27
18	72	342	-270	-32	28
19	38	371	-333	-36	29
20	0	400	-400	-40	30

| R = 409-292 C= log +0.59² MR = 40-49 MC = 10+9 Propit (A) = Revenue - Cost - 409,- 292 - 109 -0.592 Peoul- (A) = 309-2.592 Tus maximized someo and one so 107 = 30-540 2 30 - 59 I q = 30 6 units " B Profit is maximized at q = 6units, and maximum prout is $90. Also, MR = MC = $16 at this lever of output

(b R=409 - 2q² is maxinized when d o and a21 20 ƏR. = 40 - 49 20 _ - 40 - 49 - q: 10 units The maximum revenue is $200 at 10 units of output and the marginal Revenue is $0.

c) The maximum output the firm can produce to not make losses is 12 units because beyond that the firm will start incurring losses.