Mathematics for Economists Chapters 26-30 & to A6_2_2

7/31/2019 Mathematics for Economists Chapters 26-30 & to A6_2_2

1/209


2/209


3/209


4/209


5/209


6/209


7/209


8/209


9/209


10/209


11/209


12/209


13/209


14/209


15/209


16/209


17/209


18/209


19/209


20/209


21/209


22/209


23/209


24/209


25/209


26/209


27/209


28/209


29/209


30/209


31/209


32/209


33/209


34/209


35/209


36/209


37/209


38/209


39/209


40/209


41/209


42/209


43/209


44/209


45/209


46/209


47/209


48/209


49/209


50/209


51/209


52/209


53/209


54/209


55/209


56/209


57/209


58/209


59/209


60/209


61/209


62/209


63/209


64/209


65/209


66/209


67/209


68/209


69/209


70/209


71/209


72/209


73/209


74/209


75/209


76/209


77/209


78/209


79/209


80/209


81/209


82/209


83/209


84/209


85/209


86/209


87/209


88/209


89/209


90/209


91/209


92/209


93/209


94/209


95/209


96/209


97/209


98/209


99/209


100/209


101/209


102/209


103/209


104/209


105/209


106/209


107/209


108/209


109/209


110/209


111/209


112/209


113/209


114/209


115/209


116/209


117/209


118/209


119/209


120/209


121/209


122/209


123/209


124/209


125/209


126/209


127/209


128/209


129/209


130/209


131/209


132/209


133/209


134/209


135/209


136/209


137/209


138/209


139/209


140/209


141/209


142/209


143/209


144/209


145/209


146/209


147/209


148/209


149/209


150/209


151/209


152/209


153/209


154/209


155/209


156/209


157/209


158/209


159/209


160/209


161/209


162/209


163/209


164/209


165/209


166/209


167/209


168/209


169/209


170/209


171/209


172/209


173/209


174/209


175/209


176/209


177/209


178/209


179/209


180/209


181/209


182/209


183/209


184/209


185/209


186/209


187/209


188/209

A P P E N D I X A 6

Selected Answers

Chapter 2 Answers

2.5 a) all -2, d) all

2.8 = 3, = = 4x 3, d) = 2,

= + = 3.

2.9 additional revenue from the (q + output, that is, marginal revenue.

increase in consumption when national income goes up I unit.

2.1 I + + 3. + --

+ + 30).

2.12 = 9. = (I +

2.16 continuous and differentiable at =

continuous = 0,

continuous, not differentiable =

continuous and differentiable at =

2 . 2 0 6 +

+ 6. 2.22 86. XX.

2.23 increases 30.78 dollars.

2.25 9.9992s.

Chapter 3 Answers


189/209

900 SELECTED ANSWERS

3.9 a) no global or min on at 1 and min at 2 on

b) no min on , min at 0 and at 1 on

c) min at -4, at -2 min at no on

d) min at 0, at 10 on min at 0, no on

3.10 (x =3.11 = 20 = (20 = 12.50.

3.16 No positive output maximizes profit.

3.19 Elasticity equals for all prices.

3.22 = + kb), = + +

Chapter 4 Answers

4.1 a) h)(z) = + 4, g)(x) = + 19.b) h)(z) = + g ) ( s ) = +

h)(z) = =

4.2 a) inside = + 1, outside =

inside = l/x, outside + + 4,

c) inside = 2.x 7, outside =

4.3 a) h)(l) = = = 5 2x =

b) h)(z) = + =

= 2x =

4.4 a) + =

+

4 . 5

d )

4 . 9 = =

b) = l/f(l) = --(I + = -4

Chapter 5 Answers

5 1 a) 8 b) 2 e) 1 h) 125 i )


190/209

SELECTED ANSWERS 90

= =

= = (2 In

5.10 = In

5.11

5.12 a) $1870.62 $4754.17

5.13 48.05 years

5.14 =

5.15 = 3.393

5.16 a) = + +

= +

Chapter 6 Answers

6.1 Net contribution cost =

6.2C=6070. =2875. F=36.422.

6.3 = + =Or , + 3: = =4.

6.4 = = + + 3; no positive solution.

6.5 8.82 percent and 18.28 percent, respectively.

6.6 percent for white females.

Chapter 7 Answers

7.1 and

7.6 = = both decrease as

increases.


191/209

90 2 SELECTED ANSWERS

7.17 a) General solution is = + = To get an integ

solution, take = 4, then = 6 and = 3. Just change the right ha

side in the system in part a and apply the same analysis.

7.18 a = -8.

7.19 a) one, = =

7.20 a) 2, 3, 3.

7.21 a) Only the solution for iii and iv; infinitely many other solution

for the other two. Unique solution for every RHS for and infini

many solutions for every RHS for ii; or infinitely many solutions

pending the RHS for or one solution depending on the RHS

for iii.

7.23 Only

7.25 : a) 2, and 1 of the other 3, = = +

7.26 C = 0.05956 P, = 0.04702. P. F = 0.35737

7.29 a) and any of the other 3 can be if is chosen as

exogenous and set to 0, = 0.6, = 0.6, = if is the o

exogenous variable and set equal to 0, the corresponding system has i

finitely many solutions.

7.30 No, the 3 X 4 coefficient matrix has rank 2; no submatrix can have

rank 3.

Chapter 8 Answers

8 . 1

8 . 5 =


192/209

SELECTED ANSWERS 9

8.18 Carry the multiplication.

8.19 ( (

0 -6 - 1

0 13 -3 2

2 -1

8.20 =

8.21 A and defined implies has rows.A and BA defined implies B has

0 0

a symmetric matrix.


193/209



194/209

SELECTED ANSWERS

One row echelon form is

One row echelon form is

9.9 All nonsingular since det 0.

1 3

0 6

2

0

9.14 = = = = -4.

= 24: = det AR = 432; + B) = = = d e t A B =


195/209


10.12 a) acute, 45" right, 90 acute, 30 obtuse, 106.8 acute, 63.4"

10.13 a)

10.14

10.16 + + +

10.19 42.03"

10.24 expand determinant along top row

10.25 a) 1)

10.26 3.64

10.28 (I) (3+ (1 (1 + 1

10.29 no

10.30 = + 15 = + 8 = 5

10.32 no

10.33 =

= ( ) + = 2

= 10.34


196/209

SELECTED ANSWERS 9

10.38 yes; no.

10.39 a) = -1

10.40

10.41

10.42 If I increases, so does and If increases, increases and

decreases. If increases, so does and

Chapter 11 Answers

11.2 a) independent b) dependent c) independent independent

11.3 independent dependent

11.12 no yes no yesII.14 no yes no

Chapter 12 Answers

1 2 . 1 d)

+ decimal places

the digit after the decimal point in12.2 out of order.

set

second element not in original sequence

12.21 neither. closed. closed. open, closed.

12.31 None bounded.

Chapter 13 Answers


197/209


13.13 I for example.

13.23 Domain I - I

3x 7 R R yes + 7) yes

1 R

R R R

R

R R

I

1

R l / e ]

13.24 a) f(x) = = + 1 f(x) = =

f(x) = = = + x; =

Chapter 14 Answers

14.1a) = +6 =

= Y = = =

= =

= =

14.2 =

= ,

= +

14.4 a) 5400 5392.8, 5412.5

5392.798, 5412.471 = 60

14.5 a) own price elasticity =

cross price elasticity =

income elasticity =

1 4 . 6 a ) 4 . 5


198/209

SELECTED ANSWERS

14.15

141, .

14.18

14.19

14.20

14.21

427.5 19.5 14.22 I)) =

Chapter 15 Answers

15.3 2.9X

1.8607: 1.9913

15.5 = I in both cures.

15.6 a) = yes

15.8 no no -0.9449. 0.4961.

15.9


199/209


200/209


201/209


202/209


203/209


23 .15 a ) l , - 0 . 2 ;

23.17 a) + +

+ +

23.26 a)

where =


204/209

SELECTED ANSWERS

23.40 = = = 1Chapter 24 Answers

24.4 Initial position and initial velocity.

24.5 a) = + k = b) = + k

= + + 2, k = d) = k

24.9 =

24.10 a) = = +

24.13 a) = = +

24.14 = + =

24.16 = = +

24.17 = + +24.25 Equilibria at = 0 (asympt. stable) and at = 2 (unstable);

equilibria at = (unstable) and at I (asympt. stable).

24.26 a. Equilibria at = 0 (unstable) and at = k (asympt. stable);

equilibria at = 0, k (asympt. stable) and at = (unstable).

24.27 Equilibria at 0 (asympt. stable) and = I (unstable);

equilibria at (2n (asympt. stable) and at =

(unstable) all integers


205/209

25.2 = =

25.3 = =

25.6 a) = + = + = = 0.8.

=

= sin = 0, =

= =

coexistence steady state.25.8 (0,

25.9

25.12 all unstable.

25.13 Trace 0 and det 0 implies that is locally asym

totically stable.

25.16 The of Jacobian at are the pure imaginarynumbers

25.17 asymptotically stable, b. d, unstable.

25.20 a) All orbits in interior converge 3); All orbits in interior

converge to (0.6): All orbits in interior converge to (3.0).

25.24 = + = = 0.

25.28 Since Hessian of in (28).

0 is positive definite

the interior of the orthant, Fis convex and its critical point

is a global min.

Chapter 26 Answers

26.1

26.7 n!; II!


206/209


207/209


27.14 a) has a solution for

has solutions for everyhas unique solutions for every has a solution for every

27.19 a) yes, yes. no, yes, no.

Chapter 28 Answers

28.3 a) 45 X IO!, x II!.

28.4 (123) represents (132) represents

(213) represents (312) represents

(231) represents (321) represents

I represents

I (321). 1 I represents

Chapter 29 Answers

29.1 a) yes, no, yes.

yes. yes. yes; yes.

29.11 a) not open_ closed, not connected.


208/209

SELECTED ANSWERS

1.1; 1.095; 1.0955; 1.095445

1.5; 1.375; 1.4375; 1.414214.

= +

In 1.2 0.18232..

I n 2 I n 2 0 . 5 ;

30.11 = 2, = 2,

= 1.86121, = 1.86816.

30.12 a) +

= 1 + = + += +

= + +

= +

= +

+

= k = P , + abk +

= + + +

+

Appendix Al Answers

Al.1

Al.2 no lub; =

Al.6 = = a,, = 1).

Al.7 2 and + 2 implies + 1)

Appendix A2 Answers

AZ.4 a) sin 120 = = 1 2 0 = =ran 120 = 3 b = =


209/209

SELECTED ANSWERS

AZ.11 I + 0.707429, which compares we

0.707107.

Appendix A3 Answers

A3.3

A3.7 a) + i&)/2, i&)/2.

A3.8 a) 1 + sin i.

Date post:	04-Apr-2018
Category:	Documents
Upload:	jhon-ortega-garcia
View:	218 times
Download:	0 times

Mathematics for Economists Chapters 26-30 & to A6_2_2

Documents