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Q TC 0 300 1 378.227 2 453.016 3 524.529 4 592.928 5 658.375 6 721.032 7 781.061

ID: 1196705 • Letter: Q

Question

Q

TC

0

300

1

378.227

2

453.016

3

524.529

4

592.928

5

658.375

6

721.032

7

781.061

8

838.624

9

893.883

10

947

11

998.137

12

1047.456

13

1095.119

14

1141.288

15

1186.125

16

1229.792

17

1272.451

18

1314.264

19

1355.393

20

1396

21

1436.247

22

1476.296

23

1516.309

24

1556.448

25

1596.875

26

1637.752

27

1679.241

28

1721.504

29

1764.703

30

1809

31

1854.557

32

1901.536

33

1950.099

34

2000.408

35

2052.625

36

2106.912

37

2163.431

38

2222.344

39

2283.813

40

2348

41

2415.067

42

2485.176

43

2558.489

44

2635.168

45

2715.375

46

2799.272

47

2887.021

48

2978.784

49

3074.723

50

3175

51

3279.777

52

3389.216

53

3503.479

54

3622.728

55

3747.125

56

3876.832

57

4012.011

58

4152.824

59

4299.433

60

4452

A monopolist has a Fixed costs (FC) equal to $300, and its total costs (TC) are given in

Table . The (inverse) demand curve it faces in the market is described by this equation:

P = 500 - (10 )Q.

1(a). Derive the MC and ATC values using the equation MC = ^TC/^Q and ATC = TC/Q.

1(b). Draw the MC and ATC curves using the values derived for 1(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.

1(c). What is the price (PM) and quantity (QM) that the monopolist will choose in order to

maximize profit? What is their total profit from this price and quantity combination?

1(d). What is the consumer surplus when they charge the price PM from 1(c)?

1(e). If the monopolist is able to price-discriminate and charge two different prices, P1 = $200 and P2 = $310, then what is their resulting profitt? What is the consumer surplus under this price-discrimination?

Q

TC

0

300

1

378.227

2

453.016

3

524.529

4

592.928

5

658.375

6

721.032

7

781.061

8

838.624

9

893.883

10

947

11

998.137

12

1047.456

13

1095.119

14

1141.288

15

1186.125

16

1229.792

17

1272.451

18

1314.264

19

1355.393

20

1396

21

1436.247

22

1476.296

23

1516.309

24

1556.448

25

1596.875

26

1637.752

27

1679.241

28

1721.504

29

1764.703

30

1809

31

1854.557

32

1901.536

33

1950.099

34

2000.408

35

2052.625

36

2106.912

37

2163.431

38

2222.344

39

2283.813

40

2348

41

2415.067

42

2485.176

43

2558.489

44

2635.168

45

2715.375

46

2799.272

47

2887.021

48

2978.784

49

3074.723

50

3175

51

3279.777

52

3389.216

53

3503.479

54

3622.728

55

3747.125

56

3876.832

57

4012.011

58

4152.824

59

4299.433

60

4452

Explanation / Answer

a)

b)

c)

now we see that MC=MR is not exactly there in these tables which is necessary for profit maximization but it is nearly equa when Q=23 So at Q=23 P =270 and Total profit = R - TC = 6210 - 1516.309 = 4693.691

d) Consumer surplus = 0.5*(Maximum chargable price = current price)*Q = 0.5*(500-270)*23 = 2695

Q TC MC ATC 0 300.000 1 378.227 78.227 378.227 2 453.016 74.789 226.508 3 524.529 71.513 174.843 4 592.928 68.399 148.232 5 658.375 65.447 131.675 6 721.032 62.657 120.172 7 781.061 60.029 111.580 8 838.624 57.563 104.828 9 893.883 55.259 99.320 10 947.000 53.117 94.700 11 998.137 51.137 90.740 12 1047.456 49.319 87.288 13 1095.119 47.663 84.240 14 1141.288 46.169 81.521 15 1186.125 44.837 79.075 16 1229.792 43.667 76.862 17 1272.451 42.659 74.850 18 1314.264 41.813 73.015 19 1355.393 41.129 71.336 20 1396.000 40.607 69.800 21 1436.247 40.247 68.393 22 1476.296 40.049 67.104 23 1516.309 40.013 65.926 24 1556.448 40.139 64.852 25 1596.875 40.427 63.875 26 1637.752 40.877 62.990 27 1679.241 41.489 62.194 28 1721.504 42.263 61.482 29 1764.703 43.199 60.852 30 1809.000 44.297 60.300 31 1854.557 45.557 59.824 32 1901.536 46.979 59.423 33 1950.099 48.563 59.094 34 2000.408 50.309 58.836 35 2052.625 52.217 58.646 36 2106.912 54.287 58.525 37 2163.431 56.519 58.471 38 2222.344 58.913 58.483 39 2283.813 61.469 58.559 40 2348.000 64.187 58.700 41 2415.067 67.067 58.904 42 2485.176 70.109 59.171 43 2558.489 73.313 59.500 44 2635.168 76.679 59.890 45 2715.375 80.207 60.342 46 2799.272 83.897 60.854 47 2887.021 87.749 61.426 48 2978.784 91.763 62.058 49 3074.723 95.939 62.749 50 3175.000 100.277 63.500 51 3279.777 104.777 64.309 52 3389.216 109.439 65.177 53 3503.479 114.263 66.103 54 3622.728 119.249 67.088 55 3747.125 124.397 68.130 56 3876.832 129.707 69.229 57 4012.011 135.179 70.386 58 4152.824 140.813 71.600 59 4299.433 146.609 72.872 60 4452.000 152.567 74.200