............................................................................................

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.................................................................................................

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!" ..................................................................................................

#$%&' ............................................................................. (

)*+"*, -./ 01 ................................................................................. 2

!3*+" .................................................................................................. 2

, * ......................................................................................................... 4

*, 5 ............................................................................................ 4

./01 .................................................................................................. 67

./#3"PE ............................................................................................ 66

89 ....................................................................................................... 66

*+"89$:3" .................................................................... 6;

.................................................................. 6(

?'01' ................................................................................... 6@

A+'101 ............................................................................................ 6@

#B!" ................................................................................................. ;;

!"!3 ............................................................................................ ;;

!->$01C ..................................................................................... ;;

!"> ............................................................................................. ;

DEF'G0> ................................................................ ;

0>C0,H ..................................................................................... ;

> .............................................................................................. ;(

=> .......................................................................................... ;(

................................................................................................. I6

D,3" ................................................................................... I6

/"-/"',G .................................................................................... I;

/". ......................................................................................... I;

/"!3 .......................................................................................... I;

',G/"? ................................................................................... I;

C/A=,J',G/" ................................................................ I;

C/AK =,J',G/" .......................................................... II

-#B .................................................................. I

#0L0 ...................................................................................... I

#&M$,1N, .............................................................................. I

#0L0 ...................................................................................... I(

#3" .............................................................................................. I(

,.9G01N, ............................................................................. I(

O1P-F ...................................................................................... I4

P#,P-#-Q ........................................................................ ;

RS'.!T ..................................................................................... (

.SMUJ ................................................................................... (

', ...................................................................................... @

N,)/N,,VW ...................................................................................... 7

/N,X,VN, ............................................................................... ;

CJU, ................................................................................... ;

%M"'-,1< .............................................................

'%M" ........................................................................

E3PL0L- ................................................................................

#3L-Y.SMZ[EUAC , EUAB ...................................... (7

P*'\G,E5"->]" ......................................................... ((

/,"L-,1 ............................................................................ ((

"5L- .................................................................................. 2;

^F1_PL- ............................................................................ 2

`a ................................................................................................... 22

`aQ-[ ............................................................................... 22

',PL0 .......................................................................................... 22

'J-`a5 .......................................................................... 22

`aL-F .............................................................................. @;

b!-`aC/c5!1'E5"->]" .............................................. @I

b!(TX) .............................................................................................. @I

b!,&031!T1Q"1',/ :3" ........................................................ 46

>!

hI,H'

J

"#$%&'

&()*

+,"#+

[A ,/ o[/3 -,G!"p 1 - $Jq/!" 1 E E 1

,k

-.hb[1,-b>]"):J)#

;,/0&,!1

!"',1& E'-,,G,$bS#5%

J$'-,&k

I,2&34

JJJ10!"',1M>P Ek

-.'rP)

?"bS-[k

.-5./-?"Q0bS-[k

1 ].-5.E31 S 0 bS - [ "',1 $,%

J1Fk

v,GbBewF

0[%F,119'[C7&08@JK]k

0%/&9#:-

,G%M",0MJw1'&%$#k

6l CG,

Il '!"b&WP

l !">

T-#:$J&+"$/ $-,G-1''k

6l CG,

;l '!"b&W

-,,eM1DEF01-$-,G-:k

6l bS-P,'[01

Price Theory

!"#$%&

;l '!"_101

'x"-$1',-0

[%',1 *+"C> ,VW ,./ 0 ,{ M"B )*+"D,3" 1|1O

[',1*+"!3J},P.1VX0.&" h

X= f(px) ,

Px= g(x) -h

-.'[',1*+"C>XDEF'./1.$J$-

";*

";*A#,*TCGJ-,P[Cx.$J$-

";*"(

X= h(px)

Px= k(x) h

3@7&

S/MJ%:3'[%',1*+"-*, '5$G,

.Jh

X'

P'

Pe

P)

X)

Px

M

K

N

L

D S -./(Excess)

-01(Shortage)

x X)

O X' Xe

0 Ox6 Ox6 = x6x; = MN Pe / Ox; Ox; = x;x; = KL Pe

-7&+4Pe

/_O,eM*+"-*, '5C

5.10200

2100)

100

7).(

57

400100()).(( ==

=

=

X

P

P

xE

x

./,G.3C1:6$,/,~"6;SC9/3!M

k

,1 / 1 ,H O+ 89 5',1 J OSb1 *+" 5 ,G

,G589L-:/1-/5k

*O1h)).((x

p

dp

dxpE x

x

xx =

-.'['*+" _1" ,Gx b1x= @77l677p O+ )J1px=( 89

5/k

2006 == xp

3200

6100)).(( ===

x

p

dp

dxE x

x

;

-.1"XC/SJ+)-,XCP"C)'\{XL!C

.,91*+"89J1,91:9Q'[,k

1, K!3:'

.-s,1)

-.h+"5'[',1*xb152

+

=x

pxJ1k[./$G,*+"89

Iv.+wJ1!T-

-.h'[',1S%'*+"_1"nJ1,0MJ1k

Xn= apn+bpi+cy

C

#N>ON>)!N

)!N6( (TR)h$Q-E0.&" 0$J!"'T-EL-,P',1$J.P

!"$-%RS'[%

TR=Px.X

ON62(AR)h[T-%L-,P0BT

#N6@(MR)h5UJ0.&" TRP1k

MR|9" 1

[1.&k

MC = dTC/dx

)!)(>-

:!&(9#0@.!PQ

MC = MR

-. h '!" '[ % ',1 *+" 5Px =677lx C _1" -

TC = 7;7xJ1 k ,T 1 $ !" : !" 0 '+ - ./

/5k

MC = MR

MC =dTC/dx= ;7

TR = Px.x = 677xlx;

MR = dTR/dx= 677l@x

677l@x=;7 x=67 px=(7

-.hd!S501'!"$e1%',1*+"_1"Px=;7-xJ1k>_1"

1,1,1'!"$e1:TC = x; + @x + ;.k

ak ,T$e1:!"+wv

bk .+w.!T:[./k

ck /$e1

003@

,G,,1'!"&W$G0*+"8F1:k.:M/'!"&W

J1.,J-9)',b1k

},P6l="[?%Ji'!"&Wk

},P;l&19oa01$Ji'[

RGC

RG

MJ1#3"O+JQC

GLRM

5,"WG3@

1,#/ .+1!)U./,~".Q./,~"

IZ U./8081+1./8

Z S'[.+"

Z "K]1K_-b~E

6,0G@3@

px

x

D

x

Q-RF1'[%0'0CGJ-,PC#./

?@.34=AB$C

&(-X

-M9"[*, -!">E5"->]"-!"#B

)P'-&,+1 $'!"_10M+C0T-,,G

,,+1ET,1ET,$)e.1VPM1'!"_1

P#58>P+:3ET,%0:J\G0!-)18>P'$>PN,

J,/Pk

-.+#58>P',18>P

-.1C,G3"8>PJ1/PT1CP0-C,G3"!K-$1'0$,JA,3"1

!",0#-Q$J,Gk

C9!->$01A1,51

Production Function The Law of Diminishing Marginal Physical Product

Y! -G

; 67

I ;7

I

7

( I

2

@

4 7

67 I

#-G;(h8>P]9>P+0.&" '!"_%#5

'!"_T-%Y,GZ!"|9" 1-,GBT#5C>

J1C,G1.&k

MP= MPP= dx/d = f ()

Marginal physical product

X

D#.4

?@>

,(

+(

*(

)(

'(

'( 9 E 87,+*) %$?-FG.-##

l

)!-G h& '!" $-% C,G=" $J !" #5 0b

J1'!"k

TP= x = f()

O-G h5=0b '!" $-%,G%=" $J!"#

J1k

AP= x/ = f()/

&("#C

D,3"hEJJ,B#5!"',1'!"&W,=">

0,PM1'!"_1.11'!"&W.Q-k>1>:!

b-"3-k

&("#CDHX)*

,0 1e&15O,!">k

6Z '!"_1./

;Z '!"_10$-',GM1&W BFA'[ , L0 0 .&" )

!"',131C/0 $ 1.&"3Q' $JJ9wA PM1

/!"k

:O,J1>_1L00.&" '!"&W',1PM1_1>

.3:,1_1/>0"

J1'!"&W%!S-00',e'1&+"h

6Z :!C

;Z H@"'!"&WC_/QBT0b >;@,~'>-;4J1k

)!@D0"#C

C> 0 +& )C0 0 T- , '!" & QF E0 . b

'!"_1,1)$J!"#5k>:!"+1Q"C-1

11VtOk!"EBb[=BT0.&" =>I6-,~'>=I;

C/X = K/X + f(x)/X

AC AFX AVC

B&.!"@PQ

= TR TC = f(x) g(x)

,,B,1,1-,G|9sPO10C,T1',1k

TC = Total Cost TFX = Total Fixed Cost TVX = Total Variable Cost AC = Average Cost AFX = Average Fixed Cost AVX = Average Variable Cost

D / dx= f (x) g (x) = 7

f(x) = g(x)

',1K0[y,J0.&" C,T1h

MR=MC0.&" C,T1',1Py,Jh

D; / dx

;

Ba!

J$Ca)3Q3)_-tO3!Ok

,S h1 .,J % '0 1 1 y" 3!O - ,1K] '!" $e

k

Cah-bV'&+1)3QT',13!O-,1kkk

J13QEt!#1-K]k..!-o[/3&:!k

-]&&-KH1.!-,1KC/C

13Q,PIJ&+"$-,Gh

6k :E{J

;k CM1

Ik J1/''-,>Q',Pk

) S C0 ,e $-,G - / CJS $ - 1 ',P

-b0'/1M&)$P0,P)C0

3B'$f-,'10

"1 1 C

/dF9k

Q-,0j,91E5"&%EB5k

6l j,J

;l ,\,Vz"'3'1#,P

Il T$i

l T$10

l :,1FY:,1ZQ'T$0

9-t*"-j,J)J1,GE5"%',1'&1_P"baM

-1 )," $b 1 -J1

.$f-,:,"'k

:,",1 1 - KE 0 ',G $,1 1 dF %

J_1.-51Q"1$f-,k

-A1,EJ1,H1k

6l b aA - JdF9 ,.-5 1 Q" 1 $f-, E

,G'-

;l J$f-,:,"'-,G,E5"->]")b aA

Jk

0&Y%&7%&7

%EB.!x&-g-:,/C31',G/"., k'%M"

J1t5B/"F".Q,S'>1)k

%&7&

Z ,.9G01b

(Z ,1*''>

Z OS'>,1

Z,B'>,1l%

2Z ,10'

"#$-X%&'

-.h.P6777C!T-x31#&M!T-k

D!Z6777

Z6677

^Z;777

Z67777

1 .& ',P ,G .P6777 1 C ! T-6;731 #&M ! T-

J]J1b-"16;7,1,1E3PL0'31#&M!T-6777T-

.#TC0!k

:@h.,0$>$,1k.Q',91>J1,91$,1N,C>w,$

JS.S,,0k

-.hC/},Y:P,GK-ZI7777$,11!T-@'#AC

-$3R3

E-.#B0#0L0L0',1Q'%M"

0wM1&1dF9#+%.&C

-.h.,JBE;77777 N,1#&M',1!T-,e1K-kw#&M0

/.S,1#+k

67777YZ;77777$,1+

;6777767777;77777?,P-B+

/5,0L-0C"k

Y$,1N,6Z!-E?,P-BE

;67777Y6Z;77777?,P-BE

-$3R3

'),e1,dFJ%S0wM1&1)#dF9+%

1Sb-'L0k

-

F,+L0'-&"0.&" DEF'C0!DEk

oa677 $,1N, M"B0-,!T-67 1. ,1,1J1667# !T-

0-:/$

J1M',H0kK-\G,$G0',e-$,GK-$G0M!-

J1$k

(#N0$

6l,E3PL0!-,IYPZ

;l,$

>-

-.0-,FJ6777b1$

niPF )1()1 +=

nI

FP)1(

1)2

+=

Z P1(6i)nG.S,MPk

Z P16 / (6i)nG.S,ME3PL0Pk

"e@PA

J$-,''-&'.S,,G#TJ1k

))1(

1)1((

n

n

ii

iAP

+

+=

1)1(

)1((

+

+=

n

n

I

IIPA

,.P01P .SM',E3PL0P

"e@FA

)1)1(

(i

iAF

n+

= )1)1(

(+

=n

i

iFA

&.S,Pa$Q-PU,+',1'-

P=?

A

(

' ) n '" n *

A A A A

i=

P

F

n

( ' )n )" n '"

i=

!-

(X / Y , i% , n)

$-3"

$,1N,

KE3

#]

-.+

(F/P, Ik77, 6) = 6k@7

#-Q''C

#-Q'[1

C,'[1

1$

a / c = b / d a = I2 2 = I7 c = ?

b = @ 2 = 6 d = 6477 6;7

c = 7764@7 X = 6;7 + 7764@7 = 6I@7 = 77((7

!--

- !c $

cH

$

-f

P=F(P/F ,i% ,n) (P/F , i% , n) F p

F=P(F/P ,i% ,n) (F/P , i% , n) P F

P=A(P/A ,i% ,n) (P/A , i% , n) A P

A=P(A/P ,i% ,n) (A/P , i% , n) P A

A=F(A/F ,i% ,n) (A/F , i% , n) F A

F=A(F/A ,i% ,n) (F/A , i% , n) A F

-.,J$\QN,T.#k.$J.,J1,0j,J1'9k

"!/31#&M06E#7777C-J'\G,T,A!T-

6E#6k777k777J.P!T-kJ11w.,J/"k

(#N)\Q

A= F(A/F, i%, n)

( ' ) * + , 7 8 E 9 '( '' ') '* '+ ',

i= ,M

A=,((((

F='O(((O(((

F= A(F/A, i%, n) = 7777(F/A, , 6) = 7777( 2@;6 )= 672@477 T-

m!

.,J$\QN,T1Q"1'\G,:Y.,J.Z.&'k

-.hN,1,0!

-.h+,0'

gV0(

V\#h&Q

!P8.SMO1$-,UJ.!T)1

-

-.h/5,0

"\/$U,*0P-!,P0C1M',1.SMUJk#-#

J1,B#-k

PT = PA + PG

PT = 77 (P /A, , 67) + 677 (P/G, ,67)

PT = 77 ( 2;622 )+677( (;I6 )= 727;(

0

8>P3B$01$-1.&.P.S,,!

At = Atl6(6 + j) t = ; , kkk , n

,B#ldF9+#:!-

i$,1N,

j,~"B

t3!O$-#

At$-#.Pt

A6.P.S,:!-

jiji

ijAP

ntjAA

nn

t

t

++=

=+=

)1()1(1

,...,1)1(

1

1

1

jii

nAP =

+=

)1(

)( 1

),,,(1 njiAPAP =

!T',1j > 7-j = 7 -i # jMJ1sPO1J1@8>P#k,,H.,J:

"S&'-,'>"$/0%1'/:z"$-.#.,J$

P = 7777( I@I6 ) = ;646 !T-

&'-,>,G67+J1J8>PJ11+w.,J0k

73.2272721.1

50005

1

%10

1 =

=+

=

==

i

nAP

ji

!T-

7b4=DEb>5?

7b$-3"$-,N,,rEBT0.&" )k

-.h6!6;6;6

DEb3$-,C

'( 9 E 8 7,+*)'

'((((

*((((

',(((

F= ?

ie = (6 + 7(7 /;) ; - 6 = 7(747 = 74( ,VWN,

F = 67777(F/P, 74( ,67) + I7777(F/P, 74( , ( ) + 6777(F/P, 74( , )

= @I224

7biDb

0.!T: J 5 !&M $- , C '\G , M"B

J$!$,1N,jaBk

-5#&M081'EBP$-:1.1w$,1M"B

N,'!+J.S,Jj,O/N,-,Vk

5b3P3"5b3P0%,$,1N,,rEBT0.b /N,

$-

5b3P0%,?,P-B:P,G,H1$-%N,0.b ,VN,

'313P',1$,1

#h

M$-,GJ.S,-5$,C-J1!&k!$,1N,-6;J1k

C$,1N,6

!/N,6;

!,VN,11

+=

t

et

ri

"&$BQh!51

,VWN, )J,91#CJU,3",G.JS',918>P !k

U,08/,VWN,.!T:,VWN,/.11#$-3"$G,

J$CJk

Continuous Compounding

?#-' ?#-) ?#-* ?#-n

F = P (6 r/t)tn

r!/N,

t#CJU,3"

nJ1#3"k

F= P lim (6 r/t)tn =Per.n

t

F = Per.n

e = 26@;@;

F = P(F/P, r, n)

CJU,1.S,M$

F = A(F/A, ie, 6)

= (@6;67k777

-.hE,G;777771!T-N,6;Y/Z'\G,U,O1#

0)J1S+w,#Yk?,P-BZ

F= P(F/P, 6; , )

F= ;77777( @;;66 ) = I(;7

N@!09&\

6l E3PL0L-I

;l !.SML-

Il ,.9G01N,L-

l &L-^F1_P.

l %M",

09&\

HR3R

.JSC&M]$f-,'&+'L-Ek

L-:1&+'$f-,G0'$f-,J1k0+&3

M $G , - &0 1 $f-, , K] 0 )J F ,Q ',1

B A

!-> I77 ;77

!"E/ > 277 477

y+L0 I7 ;77

,/

PWA = ;77 + 477 (P/A, 67 , ) ;77 (P/F, 67 , ) = 2@@

PWB = I77 + 277 (P/A, 67 , ) l I7 (P/F, 67 , ) = 4I(

:JAJSF,/>E3PL0:J.E31k

c(@@:j$7*

J/ .!TL-:k,H$f-,',1,9,/ 11!

.P,Gk1U-- 6@777 66777

"E/ >! I677 I77

A+L0 ;777 6777

,/ 4 (

`,9,r:,Mw4-( 6@J1k

PWA= 66777 + 66777(P/F, 6 , () 6777(P/F, 6 , () + 66777(P/F, 6 , 6;)

6777(P/F, 6 , 6;) 6777(P/F, 6 , 6@) + I77 (P/A, 6 , 6@)= I@4

:J',1Bh

'(((

'E(((

'E(((

A=*'((

'E

SV=)(((

A=*'((

SV='(((

'(((

''(( ''(( ''((

R@

A=*,((

PWB= 6@777 + 6@777(P/F, 6 , 4) ;777(P/F, 6 , 4) l ;777(P/F, 6 , 6@) +

I677(P/A, 6 , 6@) = 6I@

PWA1)kkkkJ$k

$-5C0b1!-'\G,},P1[ euT 0b: J},P -

K0[ 'e k. ' $f-, : K]

-RLV\#M"KEUAC , EUAB

.SM',%1T$,$f-,1=",'>-

n = j,A,/

SV= y+L0

BT!L0-j,Ay+L-,P0kkk-@7777C

]-$/"E3PL01j,A'EL-:

/"!.SM>1k

Rc

!- > 1 ,-A+L0aS 1L-:

P BT - :3"(A/P,i%,n)L0,rEBT. - $/,*

/P*C

EUACA = ;(777(A/P, 6 ,() ;777 (A/F, 6 ,() + 66777 + @77 = 6@;

EEUACB = I(777(A/P, 67 ,67) I777(A/F, 6 ,67) + 4(77 + I77 = 6(4;

$e,SB,0JB"EUACB < EUACA .k

"#JY3@bR(i)

ROR= Rate Of Return

MARR= Minimum Attractive Rate of Return

,JC0,A1,'.1Q"1j,A%'\G,.Q

J1,91ET%0'\G,:0J/K"Bk

\!h

,G ROR > = MARR JP,\j,A

,G ROR

]h

-P +A(P/A, i%,n) + SV(P/F,i%,n) +=7

-.+'\G,6777.P-C!T-77,e#!T-

-677/5,.9G01N,),e#!T-k

l 6777 + 77(P/F,i%, I) + 677 (P/F,i%,)=7

"GRi

6l QTY|,+"O1U,*5Z

;l OS-3

Il 1C-

J1k#:46( =iJ1k

-.1,e1,H,0!

F= i

( 64Il

%16.516.05

16.046.6919.355

%5%6

46.69

=+==

=

=

=

iROR

aa

d

c

b

a

L-;l!.SML-0$1,.9G01N,5

NEUA=7

NUAB=EUAC EUAB-EUAC=7

]h

-P(A/P,i%,n)+A+SV(A/F,i%,n)+7777=7

0N#

iN,)$,1N,

MARRN,T'\G,j,A%J,*T\G,%'

/k

RORJBT'\G,%0'N,k

,GRORMARRJ1k/'\G,j,A\G,k

,GRORMARRJ1k//'\G,j,A\G,k

1$f-,w&+L-ROR

'J-1b-"L-:NPWYd!SE3PL0Z-NEUAYd!SL0

!.SMZk

,GL-:ROR $f-,%(A),e$f-,0,91(B) #-$f-, o>!J1

(A)K-$f-,0(B) J1/,"'k$f-,'&+',101L-:1

/$P*'\G,E5"->]"C .5"L-k

;0lY"#)&HG"#Cf5m

,e1,Hb-!->1G0$f-,-k$/h

,91!->1$f-,= ,/!->1$f-, + b-"$f-,-:1!->

PWX PWY NPW

6lF$f-,:,"'C31,91!->1'$f-,)$f-,-:10,GEO1

0,91,1,19G01N,"1S$f-,"/ C"JMARR

,-:1b-"ME1,1,19G01N,>$f-MARR.JS,

i/:3"$f-,:,"'/,"L-1k

Th

MARR=a%

,G ROR MARR =S'[1Q

ROR MARR =S:Q

X-Y-Z'k

WJ1/'k

&+X,Yh=SCwXY081UJ'j,A.QY>1Q"1

.,"',"[1!-k

&+Z,Yh=SCwYZ'0,/UJj,A.QY>1Q"1

.,"',/!-k

PWB

PWBZ

PWBY

PWBW

PWBX

PWC PWCW PWCZ PWCY PWCX

Z

Y

X

NPW=( MARR=a%

W

'-& ).b-" ,.9G01N,.++Tb-"=S-0U,*,G

!->1$f-,b,{-,91!->1$f-,J1$\QN,T081

F,/Jk

Q@]#@#3\"#JY3@bRk

6l C1'"$f-,CM"B'.,"'' $f-,J1,1,1 $f-,

J1,.9G01N,:,"[1k

l J&+1-1-$f-,)J,1,1$f-,!->M"Bk,G

081b-" ,.9G01N,MARR ',91 !- > ' $f-, 1

,"'.',/!->''$f-,b,{.,"'

J1k

-.+ h',0j,A-0P*'\G,E5"->]"/,"L-0$1

/dF9

,/ b-"1Q"1$--5k

j,A X PWC= ;77 7(P/F, 67 ,()+ ;77 (P/F, 67 ,() 7 (P/F, 67 ,6;)

= ;(4

PWB= 4(P/A, 67 ,6;)= (2

j,A Y PWC= 277 l 67(P/F, 67 ,6;)= (;

PWB= 6;7(P/A, 67 , 6;)= @6@

=SUJXY UJ0,/MARR=67,1,1.$1J1QkB"

JJK],/!->1j,Ak

PWB

E(( 8(( 7(( ,(( +(( *(( )(( '(( (

PWC E((8(( 7((,((+((*(()(('((

NPW=( '(M .S@+, T#-

Y

X

E'E

7+8

)79 7,)

#; h,G ,H ,0 j,A k e/ ,/ ;7,B

6l081,.9G01j,A,( Y081''$f-

JFk

#Ih

j,A)j,A:,"'AJ1k

M6h=SNPW=7) =S-.5'-QMARR,G,=SCU&T,1$f-,k

;l J5$f-,,,.9G01N,k

Il $\QN,T0,/'$f-,,.9G01N,,G(MARR) C]"0$1 ,0'$f-,

-&+,/dF9

:1&+1D-BK]k

!->b-" 6777

!1k

"/#b-" ;777

ROR= 67

!

"@nRoZ

1.&0$f-,%C1'8]3L-:k

B / C = (_P ,* ) / >Y^FZ

J_P0ME1J/P*>1,*J$9MO/k

#-L-lE3PL0

(B/C)= (_P PW / ^F PW) = (PWB / PWC)

K-L-l!.SML0

B/C= _P EUA/ ^F EUA= EUAB / EUAC

sP'L-0%,

,G B/C > = 6 B-C > = 7

.'$f-,k

,G B/C < 6 B-C 6777777 !T- Y>Z

! 7777 !T- Y>Z

!,* I7777 !T- Y,*Z

!

;/y1,o/+&j,AS1o[/3--:10j,A],V'Q_P

J1k

P*'\G,E5"->]"01 'T,AJ1k

#hF1_PL-0$1,0G0'j,AC0:3j,A:,"'^

/k

E D C B APWC 4777(777 777;7776777

PWB 4777 @2I72II72776I7

B/C 6 (6 @I6I;I6

,'3BU",1j,AY!->Z$JU",k

A - B &+-,1

PWC= 6777

PWB= II(7 B / C = I(I 6 JF B

B - C &+-,1

PWC= ;777

PWB= ;(I7 B / C = I;6 6 JF C

D - C &+-,1

PWC= ;777

PWB=677 B / C = 277 6 JF C

E - C &+-,1

PWC= 777

PWB=6(27 B / C = II7 6 FJ C

j,AC,GF$f-,:,"'C31k.&:,91'j,A:J.

J1j,A:,"'!-J1/^F1_1k

pa5_

C"-J-8+$f-,'&+',1E 0M

,1J1`a$,k

D,3"h

,1DEFC0-%L0aS" 1%L08

G`aJ1P,GbBL08:E!k

pa)#K

6l 'f!M".P,9Y,"X&T:JXM",wZ

;l G,PYi8)b,/3")'e>Z

Il b,+b,~"Y:J,P-^-0`aZ

l K->!-,?-+,~"Y&1Z

l Q-!b&S]Y-,MsQZ

0R35q

D,3" hC L00.&" C0,%',PL0

C0C

n=`a,/ Y,/ Z

0',PL0m,G5,0O10#k

BVm = P-m.D m= 6 , ; , I , , n

-.h:J%!->@7k777,/ 1!T-YaZ67A+L0-#

67777.!T-k0',PL0-!`a+/5#k

45000)70005(800005

700010

1000080000

5 ===

=

DPBV

n

SVPD

!T-

m= 7 BV7 = P = !-L0

m= n BVn = P- nD = SV A+L0

BVm= BVml6 D -',PL01Q"1',PL05$

1,cn7R5=

.&%U&T,1 - + :,91 #- # `a +L- :

`a:,/,S

2

)1(

1

+==

=

nnmSYD

n

m

bK_/Q

4,0R3

-. h:J%!->@7777,/ 1!T-67y+L0-#67777T-

.! k / 5 K- #',1',PL0 -`a +YK _/QL- 0

bZ

(SOYD)

818.55)1000080000(55

)5.0)22(10(280000

)()5.0)2((

455.11)1000080000(55

1210

)(1

552

1110

2

)1(

10000

10

80000

2

2

=+

=

+

=

=+

=

+

=

=

=+

=

=

=

=

BV

SVPSYD

mnmBV

D

SVPSYD

mnD

nnSYD

SV

n

P

m

m

5,(C0R6?

#',PL0.1VN,%,rEBT0#,`a+L-:

'QL-

k,G,#-'!`a+:,91L-:.t*-k

Declining Balance Method (DB)

)()5.0)2((

SVPSYD

mnmPBVm

+=

Dm = BVml6(d)

BVm= P(6-d)m

Dm = d.P(6-d)ml6

d.1VN,

J1'J-',),,k

,1,1',1E! \!-`a,+59+A+L0L-:

Q-A+L01,S

,/ 0>eQ',1n E !C"#A 1 !T-

$\QN,T(i%) E$-C"/0(P-SV) ,!T-

J1JQ".Qk

A = (P-SV) (A/F, i%, n)

-. :J % !- >@7777 C

paR Z

"!QP,B8+U`aL-F kM"B

1J/ '0

&(paB7rG(@0)&HG"#Cf

P,G,HC-1 $f-,' &+-E5"->]"C"-`ab,V:

,G ,1 b! kE5" - >]" - ,1 1 \ C/ c5! 1 P :

0,''$f-,k

&(61(TX)

1U+T-++TRFJ

Cash Flow Before Tax

b!0'

IZ,.9G01N,L-Yd!SE3PL0Z

NPW = 7

n - P + CFATj (P/F, i%, j)=7 i=?

j=6

iMARR '

i

aZ #-Qj,J

bZ #-Q,S

NEUA= @66I7 (A/P, 2 , )

NEUA= I;2 7 .'

$\QN,T1\$f-,2.'k

-.h'$f-,!->677777C

00@&(paI]-C0k/H:',1',"$$1]k

&(#"X6q (TS)

B"! N, `a +,rEBT 0.&" # , "! Q P,

.k

CFAT=(GI-OC)-(GI-OC-D).TR

=(GI-OC)-(GI-OC)TR+D.TR

=(CFBT)(6-TR)+D(TR)

TS=D(TR)

,G.&Pd!SPk

.++TD(TR) P*d!SG,1J-.-k

0.&" "!QP,BE3PL05EO1h

nPWTS = Dm (P/F, i%, m) (TR)

m=6

Tax Saving

00@cD

C31~E$f-,%K]',1,G$,1N,1K-(i).P!-'\G,',1

Jk0,C 6777!T-

;Zy+L0 7!T-

IZ,/ #

Z!d!S

@Z$\QN,T 6=MARR

D!Z/5,.9G01N,k

Z,G7 !$,1N,=,J.5"%1="!->67Y$O1Z) PR=677-

I=27J1k/5,.9G01N,.!T:k

^ZK]',1K-.P

NPW= 7 277l + (;; (P/A, i%, )= 7

i= ROR= ;;;;

oM

J$9MO/ k,91D!.!T1.&,.9G01N,-d!SE3PL0

.$Jk.'$f-,:\=,J1K-.Pk

#C[#C&(Nm+

1>eQ E5" - >]" ']1 Q%',GM1 ' ,

QY.$Jy+-$,C1C

-.h/:J%J1,H>eQ',1).$,,/ #k:J:

'01./1C",*T#T7777.S-,P!T-kL0/F",+1Q"1

,/3"'>-A+M1Q"1-.$J$,0#-Q!'e-b

# 1 B T67 sP :J 0 1 ,e # w 5 )J1

J$kv.+w_P$/1',/ ,eb31

'e-b,/3"'>-A+L0/:J

&7"#C

"&(0[ T

)#1#b5EUAC.,0j,91k

"#C"&(-

0[

7&"&("(

03@LRM

EUAC 6777(A/G, 67,n) 777(A/P,67,n)

SVt(A/F,67,n)

#)n(

l l l 7

6777 l 6777 6

6;(;7 @7 6;67 ;

664@7 47 6677 I

66227 6I@7 67I47

662;7 6@67 4467

66667 ;;;7 @@47 (

672@7 ;(;7 @6(7 2

67(;7 I777 2(;7 @

67@7 II27 2;67 4

67(77 I2;7 (@@7 67

67(@7 7(7 ((;7 66

-8#"/:J:0 $!>C9b aA:

18>Pk:J:$/1',/ 34:JM1Q"1-.#

1CeQL0_P

EDRV= _P3"L0 = EUACD - EUACC

EDRV>7 EUACD>EUACC .'3"

-. hJI"E/ >'.$,#477 A+L0-!T-

I77081S,/ C!T-2J1.#kFU'$J

!->;@777,/ -!T-6A+L0-#I777"E/ >-$1!T-

C!!!

.$J.V,0#-Q-5DEF'!T',1E3PL0k

H$"#C ;P ;777PW= I67777PW= 7777PW=

8>P67 ;(7777PW= I;777PW= (777PW=

PW'0.&TE,>1.&k

PW.&T&1*+",~"1.&k

'@Gm_

15j,A,/ bF5B)y+0' /]"-"

-,5::y+ /] -j,AL,\ T"-"15'[1y+ /]

C9j,AC1k

-.

..,0bF91T,Ak

P= 627k777 !-> MARR= 6I

= I777 !> N= 67 #

SV= ;7k777 y+L0

= Ik777 !

b,~"1.&j,AXY

2&7Zmq

O M P

"&("#C67777 67777 67;7

"&(N;777 64@7 6477

&'7*6; 6; 4

T

,:,~"$,&G-j,A,11-$/C1,~_1"b1

0,kG,1,>!;I7k777

A+L07k777

:J,/ 67#

",>6;7. !T-

",3"6,

!"E/ >Ik777!T-

!"C>@. :"

j,A:J;h

!->@7k777

A+L0

:J,/ #

>",@7. !T-

",3"I,

!"E/ >6k777!T-

!"C>(. :"

"J1+w#!"C>)/'E5",1,>!

Th

X,1,O+#&M:"U&T,1!"+

X6I777Y67,67,F/AZ7k7777lY67,67,A/PZ;I7k777EUACO X64;7(4

X7XI@7,!>/>j,A',1:";

X677Y,67,A/PZ@7k777EUACDX7677I(

@6I;xX7677I(x64;7(4EUACD EUACO:"#

+081!"C>,G@6I;\!.,"'%"":J,SJ1#:"

J1,,G;777J',S%"":JJB"J1J!"#:"k

![I?

B

\\\\\![W\X 5b

\\\\\![W\X 5b

I\ ![WX'

I\ ![WX)

X -.\\\\\:U.

X',Qx&QXK&K&')(Q-[1G- ![WX.c %'

')( E

c

5Y c

U.

5Y

' E

' 7

c_m

" bS-['1,~"Y,Sb,~"ZGK"C0.J\G1k

" #C8>P0JK"22

3A,SE+"

3A'a1-t

./8>P0JK"2@

#0L0

Inflation Price Inflation Cost Inflation

cb"G24

'[=./,GA#%P631#-P;,0O11K"N,)J1

JD,3"k

if = ((p; P6) / P6 ) 677

if = [K"N,YBZ

,Gh

P(t) = t C0[./=

P(t+t)= t ./=C0.J\G0[

bK"=N,t1J,1,1h

P(t+t)= P(t)(6if)

/3"C"sPO1J1.1VK",Gk

P(t+nt)= P(t)(6if)n

n0#A1$-3"t

#K"N,K

,Gifk#K"N,KJ1k

K #'./ =K #'1./k (6ifk)

6 ifk = ( K . #'./ ) / (K . #'1./ )

ifk = ( K . #'./ ) / (K . #'1./ ) l6

#./nK

Inflation Rate

#K"N,,Gif6-J1U","131'!if;-ifI-kkk#./-

P6#./J1n1.,1,1Kh

Pn= P6(6if6) (6if;) (6ifI) . (6ifn)

,GY(t),S>V./1[%0T-P(t))J1k

V= (Y(t)) / (P(t))

C"DEF0_A+-/3"O1:k

V= (Y(t6)) / (P(t6)) = (Y(t;)) / (P(t;)) = (Y(tI)) / (P(tI))

Kq?

J10_O+,.S,.PET-0b Yk'Q[Z

@DR3@Kq+

T-,SbU&T,1$

J1.1VK"N,,Gk

Y'(t)= D(t) Y(t)

7&UVQq1

dSJ[%./.&,rEBT0JC1 %="o[/3./

DEF0_O+-bS-[0-,G-,677BT

JkG#,"-00_O+k

#h#,1K,GE%./,G6I2)I777-##6I@;L+6;777#

J1k#',1./dSJ6I21.,1,1h

(6;777 / I777 ) 677 = 77

,1,1#',1dSJ:,116771Sk

dSJ6n',1MJD,3",0j,J1bS-[0$-,Gk

In = ((Pn6 / PK6) + (Pn; / PK;) + . + (Pnm / PKm)) / M

K#

n,1#

M,1,B 3"

Pnm?0[T-%./m#n

PKm?0[T-%./m#(K)

.$JP,G,H'-& EC0-sPO1kw[%./,G

1[JjaB,0b1sPO1J1+10,9k

In = ((Pn6W6 / PK6) + (Pn;W; / PK;) + . + (PnmWm / PKm)) / (W6+ W; +

+ Wm)

WiKa0%,0-U,*

Price Index

UVQ

+,Q:7*7&UVQWPIq4

,G$>./>!1$-

' >b[5)E/]l$J-,\{lQ&b[5l-,wb[5

CEP

'>EPb[5lb[:Jl#>K0!-C/El'>EP,{b[5l-+-/T

J1k

:!7&UVQCPIq5

J1=

'!:1[,Sb,0#-Q647-64@@Y$,./dSJ,1

CPIZ

CPI -CPI-CPI -

7k(2@

7k(;6

7k@2

7k6

7k6;

7k(6

7k7

7k(2

7kI(

7kII

7kI;6

7.I67

7kI7

7k;46

7k;2@

642

642

642(

6422

642@

6424

64@7

64@6

64@;

64@I

64@

64@

64@(

64@2

64@@

6k6;2

6k66(

6k67

6k746

6k72(

6k7@

6k7;4

6k777

7k4(7

7k466

7k@(7

7k@;

7k244

7k2;

64(7

64(6

64(;

64(I

64(

64(

64((

64(2

64(@

64(4

6427

6426

642;

642I

;kI@6

6k@

6kI@2

6k76

6kI@2

6k;@

6k;@

6k;@

6k;;

6k;2

6k;;4

6k6@(

6k6

6k6

647

64

64@

644

647

646

64;

64I

64

64

64(

642

64@

644

' #hESFJ},P;77k777011#6,/'\G

+BT -,_/Q1]#'-67].Q:0_1,,

',SM&T-k31,,,,0,H5:0./,*T#T

6(k777.#k=O1:0./8>PN,,G

F= ;k777k777(f/p, 6%, )= ;k777k777(6+ 6k ) = Ik@7k@;4 #

,S',1,*T#T671:0,;k777Y6(k777Z671/.S,#

K"N,:P,G,H6@ J:wC

E1-' &W0?0,%},P677777$/.P#

b67/.S,01#kK-$,1@.$JP,G,Hk-.1VK"N,,G

!K/".1.1V#U&T,1C\!)J,#:{--.S3

/,~".1V#U&T,1k

.1V#1$Q-C,Q1'Q#1$Q-C,Q",0#-Q

(:B#L-#

0M

)#h#;:B#L-#

@DM

6

;

I

6;7777

6;7777

6;7777

(6k7)l6= 7k4;

(6k7)l;= 7k4727

(6k7)lI= 7k@(I@

66;@@

67@@7

67I((

(

2

@

4

67

6;7777

6;7777

6;7777

6;7777

6;7777

6;7777

6(;7777

(6k7)l= 7k@;;2

(6k7)l= 7k2@I

(6k7)l(= 7k2(;

(6k7)l2= 7k2672

(6k7)l@= 7k(2(@

(6k7)l4= 7k((

(6k7)l67= 7k(6I4

4@2;

47;7

@4

@;@

@6;6(

22I;

446@

:j$:0#c&Dv

,1=",>

:1O1i)i')if

,BC0_O+Y,*T#TZC&M,Sb'-,.1V#-'Q#

Q-',11,e0_O+)&k#-'Q#C1'-&1Q"1

_O+.1VY,B#Z-D!./&C0#3)MJ-kkk-$/5

,,B'-&k

"f-fC#'-,nO10&Kkkk

D!l/5'Q#U&T,1$f-,:#TC0#3k

l#-#K"=N,,G(-31#2:$Q-C,Q/J1

-

aC;= 77 / (6 7k7(); = 77k4@ #>

aCI= 77 / (6 7k7()I = I22@k;@2 #>

K"N,,V".5"9"Kw'!'0d!S

aC(= 77 / (6 7k7()I (67k72)I = I7@k;72 #>

aC2= 77 / (6 7k7()I (67k72) = ;@@;kI2 #>

aC@= 77 / (6 7k7()I (67k72) = ;(4Ik@(( #>

.1E;7777'Q#-..1V#+',1'\G,#

1SC&MkJS,0MJ|1O.1V#1"0$f-,$Q-C,Qk

cb(f)

1,PN,0.&" K"N,fC9k

-.h[dSJ#;7731#-;6(J1k/5K"N,k

a

abf

)( =

a#dSJ

b31#dSJ

08.0200

)200216(=

=f

)((((

+)+,O)E*

' ) * + , 7 8 E

SU L6#.!##.[

+((+O9E+ *88EO)E

8

*,*'O'(

**((O'()

*(E+O)(8

)EE)O+*8

)79*OE77

-.,gSJI0#62(1;6(.$k/5K"N,k

%1.7%71

176

2161216)1(176 33

==

=+=+

ff

ff

cC&(NL00:j$cD@M

J1K"N,,GY0,/oaBZ-'b5,]"

0wb"Gif

',gN,ifK"C/c5E031$\QN,T0.&" k

,GP-,*T#TL0FtL0b1K"031tJ1#k

P= Ft / (6f)t (6i)t

P= Ft / (6if)t (6i)t (6f)t = (6if)t

if = i + f + if

#h$\QN,T,G67K"N,-/5',gN,J1k

If = 67 + + 777 = 76

)#@Dh#;

F1-J1Jb-#-',1$,./'SJ+$G,

j,91".1VU,*0/",e#./1K"1Q"1#&M./

J$,0k

098.14.195

)4.1951.214(1=

+=CPI

K./Y#6I2(Z = I22777 74@6 = I@4777

c0&Y:3

,',G$0./dSJ%/1C"K"C>k[>)./dSJ

C9#[C/>1.&[%'Qk3h

c(Types of Inflation)

6k *+"890JK"(Demand-Pull Inflation)

;k >9P0JK"(Cost Push Inflation)

;

Ik J#~J,~"-!",~"UQ"K"k

x!c*(Inefficiency)

1 /-L01_1 0r31 JUQ?*:`K

iP&-,1-$0"'$1,*TC,

#1>'M1)./tOk&1C,K-/$:'K")

St*"CP

C,51

!"T

'M1,T

Recession Slump Expansion Boom

1

!"N,8>P

8'M1

|-

!",T

'M1T

o,+"']"-%.#k

HU(V&(Gross National product (GNP)-SE!" E-1'!"ibS-[L0?/])E!S!"

.:3$-%90^Sk"1[J)E!S!")D,3":1Q

EM!,{b1-,9 )i\{ )S>JQ )C, +'

/&H[n

6. G. J. Thuesen, W. J. Fabrychy, Engineering Economy, (Prentice-Hall

international Series in Industrial and Systems Engineering), Prentice-

Hall College Div; ISBN: 76I7;@6;X; 4 edition, ;777.

;. James L. Riggs, David D. Bedworch, Sabah U. Randhawa,

Engineering Economic, McGraw-Hill, Higher Education, ISBN;

77246;;@, th edition, 644(.

I. Gerald W. Smit, Engineering Economy: Analysis of Capital

Expenditures, Iowa state university press, ISBN: 7@6I@7I@; th

edition, 64@2.

. Eugene Lodewick Grant, William B. Areson, William G. Ireson,

Principle of Engineering Economy, @th edition, John Wiley & Sons;

ISBN: 726(I;(X; 6447.

. Leland T. Blank, Anothony J. Tarquin, Engineering Economy,

McGraw-Hill, Series in Industrial Engineering and Management

science, McGraw-Hill Collage Div; ISBN; 772;I;I4, th edition,

;776.

(. J. C. Sprague, J. D. Whittaker, Economic Analysis for Engineers and

Managers, Prentice-Hall, ISBN; 76I;;7(, 64@.