Question

Atemis tine actions a)= 1069-2 ts cost functions Co 104 15 Using Exotice the love of revenue total cost and profit for the fem for 0,12 24 Dome the poolt mauming up and the mu profit for the form b). Using Exceleratograph of the protecure and determine the profit-ming val of output (You don't need to submit the graph) C. The tum meginal revenue function MR=104 4q and the marginal con M3Ung Esculto MR and MC 0.1.2 24 Vanity that the "MRMC determines the same protturn output as you found in part At you come the spreadsherswer the following us Not When you need to end the dots, vound your arsWits to the nearest tenth is woed What is the of what What is the who? What is the tool who Wha w What is the fun when? Wusstwo when we Womed What is the wo? What the What i otprofiel What the value of What the MR Wat the MC From the Yound that the MRMC determine the same promete you found in a

please put a number by the answer.

Answer 1

a)

Given the revenue and cost functions, we can calculate revenue and cost using for q = 0, 1, 2....24

If q = 0, then:

C = 104 + 6*0+1.5(0)2 = 104

If q = 1, then:

R = 104 * 1 -2(1)2 = 104 – 2*1 = 104 – 2 = 102

Similarly, we'll calculate the values for R and C for q = 0, 1,2.....24 in the given table. Also, we know that

Profit = Revenue - Cost so, the profit values are also computed for all q:

q	R(q)= 104q - 2q^2	C(q)= 104 + 6q + 1.5q^2	Profit = R -C
0	0	104	-104
1	102	111.5	-9.5
2	200	122	78
3	294	135.5	158.5
4	384	152	232
5	470	171.5	298.5
6	552	194	358
7	630	219.5	410.5
8	704	248	456
9	774	279.5	494.5
10	840	314	526
11	902	351.5	550.5
12	960	392	568
13	1014	435.5	578.5
14	1064	482	582
15	1110	531.5	578.5
16	1152	584	568
17	1190	639.5	550.5
18	1224	698	526
19	1254	759.5	494.5
20	1280	824	456
21	1302	891.5	410.5
22	1320	962	358
23	1334	1035.5	298.5
24	1344	1112	232

So, we can see that the maximum profit of the firm occurs when the output of the firm is 14 units and the profit of the firm is 582 units.

b)

Profit = R-C 700 600 500 400 300 200 100 0 5 10 15 20 25 30 -100 -200

So, from the graph also, we can see that the profit maximizing output is q = 14 units.

c)

If q = 0,

and

Similarly, we'll find values for all other q in the given table:

q	R(q)= 104q - 2q^2	C(q)= 104 + 6q + 1.5q^2	Profit = R -C	MR= 104 - 4q	MC = 6 + 3q
0	0	104	-104	104	6
1	102	111.5	-9.5	100	9
2	200	122	78	96	12
3	294	135.5	158.5	92	15
4	384	152	232	88	18
5	470	171.5	298.5	84	21
6	552	194	358	80	24
7	630	219.5	410.5	76	27
8	704	248	456	72	30
9	774	279.5	494.5	68	33
10	840	314	526	64	36
11	902	351.5	550.5	60	39
12	960	392	568	56	42
13	1014	435.5	578.5	52	45
14	1064	482	582	48	48
15	1110	531.5	578.5	44	51
16	1152	584	568	40	54
17	1190	639.5	550.5	36	57
18	1224	698	526	32	60
19	1254	759.5	494.5	28	63
20	1280	824	456	24	66
21	1302	891.5	410.5	20	69
22	1320	962	358	16	72
23	1334	1035.5	298.5	12	75
24	1344	1112	232	8	78

So, we see that Marginal revenue(MR) equals Marginal Cost(MC) i.e. MR = MC = 48 when the output of the firm is 48 units.

This is the same profit maximizing output found in part a)

From the spreadsheet, we can see that:

1. The value of R when q = 8 is 704.

2. The value of C when q = 8 is 248.

3. The value of profit when q = 8 is 456.

4. Fom the revenue and cost function, we can compute the profit function as:

P = R -C

So, at q = 8:

5. The value of MR when q = 8 is 72.

6. The value of MC when q= 8 is 30.

Now, the profit is maximised when q = 14 so, at this level of output:

7.The value of R is 1064.

8.The value of C is 482.

9.The value of profit is 582.

10. The value of MR is 48.

11. The value of MC is 48.

So, at profit maximizing level of output, MR = MC.