Question

A monopolist has its total costs (TC ) of production given in Table 3. The (inverse) demand curve it faces in the market is described by this equation:

P = a − bQ = 3, 000 − (31.15)Q.

Table 3: Total Costs for a Monopolist

Q

TC

Q

TC

0	800			21	6243.2
1	1131.2			23	6977.6
2	1409.6			23	7810.4
3	1642.4			24	8748.8
4	1836.8			25	9800
5	2000			26	10971.2
6	2139.2			27	12269.6
7	2261.6			28	13702.4
8	2374.4			29	15276.8
9	2484.8			30	17000
10	2600			31	18879.2
11	2727.2			32	20921.6
12	2873.6			33	23134.4
13	3046.4			34	25524.8
14	3252.8			35	28100
15	3500			36	30867.2
16	3795.2			37	33833.6
17	4145.6			38	37006.4
18	4558.4			39	40392.8
19	5040.8			40	44000

20

5600

3(a) Question: Derive the MC and ATC values using the equation MC = ∆T C/∆Q and AT C = T C/Q.

3(a) Answer:

3(b) Question: Draw the MC and ATC curves using the values derived for 3(a). Draw the inverse demand curve and its corresponding MR curve. Note: for the MR curve, be sure to use the equation learned in class, MR = a − 2bQ.

3(b) Answer:

3(c) Question: What is the price (PM) and quantity (QM) that the monopolist will choose in order to maximize profit?

3(c) Answer:

3(d) Question: What is their total profit from the price and quantity combination in 3(c)?

3(d) Answer:

3(e) Question: What is the consumer surplus when they charge the price PM from 3(c)?

3(e) Answer:

Answer 1

a) I've calculated MC and ATC in the table below. I've also calculated price based on the inverse demand formula: 3000 - 31.15Q and the Marginal revenue based on the formula: 3000 - 62.3Q.

Q	TC	ATC	MC	Price	MR
0	800			3000	3000
1	1131.2	1131.2	331.2	2968.85	2937.7
2	1409.6	704.8	278.4	2937.7	2875.4
3	1642.4	547.4667	232.8	2906.55	2813.1
4	1836.8	459.2	194.4	2875.4	2750.8
5	2000	400	163.2	2844.25	2688.5
6	2139.2	356.5333	139.2	2813.1	2626.2
7	2261.6	323.0857	122.4	2781.95	2563.9
8	2374.4	296.8	112.8	2750.8	2501.6
9	2484.8	276.0889	110.4	2719.65	2439.3
10	2600	260	115.2	2688.5	2377
11	2727.2	247.9273	127.2	2657.35	2314.7
12	2873.6	239.4667	146.4	2626.2	2252.4
13	3046.4	234.3385	172.8	2595.05	2190.1
14	3252.8	232.3429	206.4	2563.9	2127.8
15	3500	233.3333	247.2	2532.75	2065.5
16	3795.2	237.2	295.2	2501.6	2003.2
17	4145.6	243.8588	350.4	2470.45	1940.9
18	4558.4	253.2444	412.8	2439.3	1878.6
19	5040.8	265.3053	482.4	2408.15	1816.3
20	5600	280	559.2	2377	1754
21	6243.2	297.2952	643.2	2345.85	1691.7
22	6977.6	317.1636	734.4	2314.7	1629.4
23	7810.4	339.5826	832.8	2283.55	1567.1
24	8748.8	364.5333	938.4	2252.4	1504.8
25	9800	392	1051.2	2221.25	1442.5
26	10971.2	421.9692	1171.2	2190.1	1380.2
27	12269.6	454.4296	1298.4	2158.95	1317.9
28	13702.4	489.3714	1432.8	2127.8	1255.6
29	15276.8	526.7862	1574.4	2096.65	1193.3
30	17000	566.6667	1723.2	2065.5	1131
31	18879.2	609.0065	1879.2	2034.35	1068.7
32	20921.6	653.8	2042.4	2003.2	1006.4
33	23134.4	701.0424	2212.8	1972.05	944.1
34	25524.8	750.7294	2390.4	1940.9	881.8
35	28100	802.8571	2575.2	1909.75	819.5
36	30867.2	857.4222	2767.2	1878.6	757.2
37	33833.6	914.4216	2966.4	1847.45	694.9
38	37006.4	973.8526	3172.8	1816.3	632.6
39	40392.8	1035.713	3386.4	1785.15	570.3
40	44000	1100	3607.2	1754	508

b) To draw the curves, I've taken note of the fact that both ATC and MC first reduce and then increase. MC intersects ATC at around Q=15 (from the table). After that, both the curves increase.

MR and Inverse demand curve both have 3000 as their Y intercept. And MC intersects MR approximately at Q=27. Price at this quantity is approximately 2159. This has all been noted from the table above.

c) Profits are maximized when MR = MC. As mentioned, this approximately happens at P_m = 2159 and Q_m = 27.

d) Total Profit = Total Revenue - Total Cost

Total Revenue = 27*2159 = 58,293

Total Cost = 12,270 (from the table)

So Total Profit = 58,293 - 12,270 = 46,023

e) To compute the consumer surplus, see the graph.

It is the area of the triangle above the price line (the dotted line at 2158 price) and below the demand curve.

The height of this triangle is 3000-2158=842

The base is equal to 27 (look at the x-axis).

So by just using the formula for the area of a triangle, we get the following Consumer Surplus (CS)

So Consumer Surplus = 11,367