Question

The firm’s revenue function is R=250q-8q² , cost function is C=10q+12q².

1. Use Excel to calculate the firm’s revenue, cost, and profit for q = 1 to q = 20 in increments of 1.Using Excel’s Charting tool, draw the graph of the profit curve and determine the profit maximizing level of output.

2. Based on these calculations, what output must you choose? Create columns in spreadsheet for MR and MC and verify that MR = MC at the profit-maximizing output level.

3. Now assume that you hire a manager who is paid 10% of the revenue and the manager wants to maximize revenue as well. How much output does the firm produce now? What is marginal revenue at this output level?

4. Now suppose that the firm 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. What output does the firm produce now?

Answer 1

a) Given that cost function is C=10q+12q2 and revenue function is R=250q-8q2, we draw the following table

Quantity	Revenue	Cost
1	242	22
2	468	68
3	678	138
4	872	232
5	1050	350
6	1212	492
7	1358	658
8	1488	848
9	1602	1062
10	1700	1300
11	1782	1562
12	1848	1848
13	1898	2158
14	1932	2492
15	1950	2850
16	1952	3232
17	1938	3638
18	1908	4068
19	1862	4522
20	1800	5000

Profit is maximum when Q = 6

b) MR = dTR/dq = 250 - 16q and MC = dTC/dq = 10 + 24q

Quantity	Revenue	Cost	MR	MC	Profit
1	242	22	234	34	220
2	468	68	218	58	400
3	678	138	202	82	540
4	872	232	186	106	640
5	1050	350	170	130	700
6	1212	492	154	154	720
7	1358	658	138	178	700
8	1488	848	122	202	640
9	1602	1062	106	226	540
10	1700	1300	90	250	400
11	1782	1562	74	274	220
12	1848	1848	58	298	0
13	1898	2158	42	322	-260
14	1932	2492	26	346	-560
15	1950	2850	10	370	-900
16	1952	3232	-6	394	-1280
17	1938	3638	-22	418	-1700
18	1908	4068	-38	442	-2160
19	1862	4522	-54	466	-2660
20	1800	5000	-70	490	-3200

Profit is maximum when Q = 6. At this level, MR = MC = 154 and profit = 720

c) To maximize revenue we find the output level at which MR = 0

This happens when q = 16, Though marginal revenue is not zero but -6, because we take only positive integers as output level. Revenue is maximized at 1952.

d) Losses started to occur when q rises beyond 12. Hence output from 1 to 12 will earn positive profits or at most no profit.