Question

A monopolist has its total costs (TC ) of production given in Table 4. The (inverse) demand curve it faces in the market is described by this equation: P = a − bQ = 5, 000 − (40)Q.

Q	TC			Q	TC
0	800			21	13345.4
`1	1181.4			22	14827.2
2	1531.2			23	16453.8
3	1857.8			24	18233.6
4	2169.6			25	20175
5	2475			26	22286.4
6	2782.4			27	24576.2
7	3100.2			28	27052.8
8	3436.8			29	29724.6
9	3800.6			30	32600
10	4200			31	35687.4
11	4643.4			32	38335.2
12	5139.2			33	42531.8
13	5695.8			34	46305.6
14	6321.6			35	50325
15	7025			36	54598.4
16	7814.4			37	59134.2
17	8698.2			38	63940.8
18	9684.8			39	69026.6
19	10782.6			40	74400
20	12000

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

3(b). Draw the MC and ATC curves using the values derived for (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(c). What is the price (PM) and quantity (QM) that the monopolist will choose in order to maximize profit?

3(d). What is their total profit from the price and quantity combination in (c)? 3(e). What is the consumer surplus when they charge the price PM from (c)?

PLEASE THE OTHER ANSWERS ARE WRONG, MAY YOU DOUBLE CHECK THIS A FINAL. THANKS.

Answer 1

3.

(a)

The marginal cost is the change in total cost due to one unit change in output. The average total cost is the cost per unit of output. The two formulas are MC = ∆T C/∆Q and ATC = TC/Q.

Using these two formulae the MC and ATC is calculated below

Q	TC	MC	ATC
0	800.0
1	1181.4	381.4	1181.4
2	1531.2	349.8	765.6
3	1857.8	326.6	619.3
4	2169.6	311.8	542.4
5	2475.0	305.4	495.0
6	2782.4	307.4	463.7
7	3100.2	317.8	442.9
8	3436.8	336.6	429.6
9	3800.6	363.8	422.3
10	4200.0	399.4	420.0
11	4643.4	443.4	422.1
12	5139.2	495.8	428.3
13	5695.8	556.6	438.1
14	6321.6	625.8	451.5
15	7025.0	703.4	468.3
16	7814.4	789.4	488.4
17	8698.2	883.8	511.7
18	9684.8	986.6	538.0
19	10782.6	1097.8	567.5
20	12000.0	1217.4	600.0
21	13345.4	1345.4	635.5
22	14827.2	1481.8	674.0
23	16453.8	1626.6	715.4
24	18233.6	1779.8	759.7
25	20175.0	1941.4	807.0
26	22286.4	2111.4	857.2
27	24576.2	2289.8	910.2
28	27052.8	2476.6	966.2
29	29724.6	2671.8	1025.0
30	32600.0	2875.4	1086.7
31	35687.4	3087.4	1151.2
32	38335.2	2647.8	1198.0
33	42531.8	4196.6	1288.8
34	46305.6	3773.8	1361.9
35	50325.0	4019.4	1437.9
36	54598.4	4273.4	1516.6
37	59134.2	4535.8	1598.2
38	63940.8	4806.6	1682.7
39	69026.6	5085.8	1769.9
40	74400.0	5373.4	1860.0

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b)

The ATC and MC depicted below

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c)

The equilibrium occurs where MR=MC, this occurs at Qm=29 which has corresponding Pm=3840. Substitute Qm=29 in demand function.

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d)

The total profit of the firm is given as

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e)

The consumer surplus is the area surrounded by price line demand curve and the axis upto equilibrium quantity. Then it is the area of the triangle ABC in figure below

Therefore,