Balacing Costs and Benefits

7/18/2019 Balacing Costs and Benefits

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Quick recap

What is microeconomics?

Limited resources and market

DemandSupply

Market equilibrium

Elasticity



Chapter 3

Balancin Costs and Bene!its

McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc !ll"ights "eser#e$





Ma#imi$in &et Bene!it

Net benefit ' total bene!it minus total cost

"otal cost must include opportunity cost

Opportunity cost : the cost associated(ith !oreoin the opportunity to employ aresource in its ne#t best alternati)e use

*iht decision is the choice (ith thereatest di!!erence bet(een total bene!itand total cost

3%+



Car *epair E#ample'Bene!it Schedule

Mechanic,s time isa)ailable in one%hourincrements

Ma#imum repair timeis - hours

"he more time the car

is repaired. the moreit is (orth

"able 3/0' Bene!its o! *epairin 1ourCar

*epair "ime

2ours4

"otal Bene!it

254

6 6

0 -07

8 0076

3 0-66

+ 09:7

7 88:6

- 8+;7

3%7



Car *epair E#ample'Cost Schedule

"able 3/8' Costs o! *epairin 1our Car

*epair"ime

2ours4

Cost o! Mechanic and<arts

254

Lost Waes !rom<i$$a Deli)ery =ob

254

"otalCost

254

6 6 6 6

0 0+6 06 076

8 377 87 3;6

3 -+7 +7 -96

+ 0667 :7 06;6

7 0++6 006 0776

- 0976 076 8066

3%-



Car *epair E#ample'Ma#imi$in &et Bene!it

o( should you decide ho( many hoursis the >riht number to ha)e your car

repaired?*ecall that e)ery hour in the shop (ill

brin both bene!its and costs

Choose the number o! hours (herebene!its e#ceed costs by the reatestamount

3%:





"able 3/3' "otal Bene!it and "otal Cost o!*epairin 1our Car

*epair "ime

2ours4

"otal Bene!it

254

"otal Cost

254

&et Bene!it

254

6 6 6 0

0 -07 076 465

8 0076 3;6 770

3 0-66 -96 910

+ 09:7 06;6 895

7 88:6 0776 720

- 8+;7 8066 385

Car *epair E#ample'"he *iht Decision

3%9



"able 3/3' "otal Bene!it and "otal Cost o!*epairin 1our Car

*epair "ime

2ours4

"otal Bene!it

254

"otal Cost

254

&et Bene!it

254

6 6 6 0

0 -07 076 465

8 0076 3;6 770

3 0-66 -96 910

+ 09:7 06;6 895

7 88:6 0776 720

- 8+;7 8066 385

Best

Choice

Car *epair E#ample'"he *iht Decision

3%06



+-7

Car *epair E#ample'@raphical Approach

2iure 3/04

Data !rom "able 3/3 aresho(n in this raph

Costs are in red bene!its

are in blue "he best choice is (here

bene!its costs and thedistance bet(een them

is ma#imi$ed "his is at 3 hours. net

bene!it 5906

"otalBene!it."otal Cost254

*epairours

0 8 3 + 7 -

+66

;66

0866

0-66

8666

8+66

:06

906

Best Choice

3%00



Ma#imi$in &et Bene!it'inely Di)isible Actions

Many decisions in)ol)e actions that aremore !inely di)isible

E// mechanic,s time a)ailable by theminuteFn these cases (e can use bene!it and cost

curves rather than points or a schedule to

make the best decisionGnderlyin principle is the same' ma#imi$e

net bene!it

3%08



Car *epair E#ample'inely Di)isible Bene!it

ori$ontal a#ismeasures hours o!mechanic,s time

Hertical a#ismeasures in dollarsthe total increase in

your car,s )alueB24-7+%+68

"otal Bene!it254

ours 2H 4

2a4' "otal Bene!it

6 0 8 3 + 7 -

-0+

0-68

88:6

B

3%03



Car *epair E#ample'inely Di)isible Cost

Hertical a#ismeasures total costin dollars

Fncludes opportunitycost

C24006I+68

6 0 8 3 + 7 -

076

-96

0776

ours 2H 4

2b4' "otal Cost

"otal Cost254

C

3%0+



Car *epair E#ample'inely Di)isible &et Bene!it

Best choice is 3/+hours o! repair.ma#imi$es net bene!it

&et bene!it (ith !inelydi)isible choices isreater than inpre)ious e#amplemore !le#ibility allo(syou to do better

;3-/+6

0:-0/86

"otalBene!it"otalCost254

2c4' "otal Bene!it )ersus "otalCost

6 0 8 3 + 7 -

ours2H 4

3/+

B

C 98+/;6

3%07



&et Bene!it Cur)e2iure 3/34

Can also raph thenet bene!it cur)e

Hertical a#is sho(sB%C. net bene!it

Best choice is thenumber o! hours that

corresponds to thehihest point on thecur)e. 3/+ hours

6 0 8 3 + 7 -

98+/;6

ours 2H 4 3/+

&etBene!it254

B – C

3%0-



"hinkin on the Marin

"hinkin like an economist Another approach to ma#imi$in net

bene!itsCapture the (ay that bene!its and costs

chane as the le)el o! acti)ity chanes Just a little bitFor any action choice X, the marginal units

are the last ∆ X units, where ∆ X is thesmallest amount you can add or subtract

3%0:



Marinal Cost

"he marginal cost o! an action at an acti)ityle)el o! K units is equal to the e#tra costincurred due to the marinal units. di)ided bythe number o! marinal units

X

X X C X C

X

C MC

∆

∆−−=

∆

∆=

)()(

3%0;



Car *epair E#ample'Marinal Cost

Marinal cost measures the additionalcost incurred !rom the marinal units 2∆4o! repair timeF! C24 is the total cost o! hour o! repair

(ork. the e#tra cost o! the last ∆ hours is∆C C24 C2%∆4

"o !ind marinal cost. di)ide this e#tra costby the number o! e#tra hours o! repairtime. ∆

3%09



Car *epair E#ample'Marinal Cost

So the marinal cost o! an additional hour o!repair time is'

Gsin the data !rom "able 3/8. i! 3. (e see'

H

H H C H C

H

C MC

∆

∆−−=

∆

∆=

)()(

3103806901

)13()3(=−=

−−=

C C MC

3%86



Car *epair E#ample'Marinal Cost Schedule

"able 3/7' "otal Cost and MarinalCost o! *epairin 1our Car

*epair"ime

2ours4

"otal Cost254

Marinal Cost 2MC 425hour4

6 6 %

0 076 076

8 3;6 836

3 -96 306

+ 06;6 396

7 0776 +:6

- 8066 776

3%80



Marinal Bene!it

"he marginal benefit o! an action at anacti)ity le)el o! K units is equal to the e#trabene!it produced due to the marinal units.di)ided by the number o! marinal units

X

X X B X B

X

BMB

∆

∆−−=

∆

∆=

)()(

3%88



Car *epair E#ample'Marinal Bene!it

Marinal bene!it measures the additionalbene!it ained !rom the marinal units

2∆4 o! repair time"his parallels the de!inition and !ormula

!or marinal cost

3%83



Car *epair E#ample'Marinal Bene!it

"he marinal bene!it o! an additional hour o!repair time is'

Gsin the data !rom "able 3/0. i! 3. (e see'

H

HHBHB

H

BMB

∆

∆−−=

∆

∆=

)()(

450115016001

133=−=

−−=

)()( BBMB

3%8+



Car *epair E#ample'Marinal Bene!it Schedule

"able 3/-' "otal Bene!it and Marinal Bene!ito! *epairin 1our Car

*epair "ime2ours4

"otal Bene!it254

Marinal Bene!it 2MB425hour4

6 6 %

0 -07 -07

8 0076 737

3 0-66 +76

+ 09:7 3:7

7 88:6 897

- 8+;7 807

3%87



Marinal Analysis and BestChoice

Comparin marinal bene!its and marinalcosts can sho( (hether an increase ordecrease in a le)el o! an acti)ity raises orlo(ers the net bene!itFncrease le)el i! MB o! doin so is reater

than MC i! MC o! last increase (as

reater than MB. decrease le)el At the best choice. a small chane in

acti)ity le)el can,t increase the net bene!it

3%8-



Marinal Analysis and BestChoice

"able 3/:' Marinal Bene!it and MarinalCost o! *epairin 1our Car

*epair"ime

2ours4

MarinalBene!it 2MB4

25hour4

MarinalCost 2MC 4

25hour46 % %

0 -07 076

8 737 836

3 +76 306

+ 3:7 N 396

7 897 N +:6

- 807 N 776

Best

Choice

3%8:



Marinal Analysis (ithinely Di)isible Actions

Can conduct the same analysis i! choices are!inely di)isible by usin marinal bene!it andmarinal cost cur)es

Deri)e marinal bene!it and marinal cost !romtotal bene!it and total cost cur)es

Marinal bene!it at H hours o! repair time isequal to the slope o! the line dra(n tanent to

the total bene!it !unction at pointGsually called simply the >slope o! the total

bene!it cur)e at point D

3%8;



Marinal Bene!it

Gsin Calculus

"his is the slope o! the "otal Bene!itCur)e B24/

( ) ( )dHHdBHMB =



Car *epair E#ample'inely Di)isible Marinal Bene!it

Let ∆O the smallest possible chane in hourso! car repair

Addin the last ∆P o! repairs increases total

bene!it !rom point to point D in iure 3/+ 2onthe ne#t slide4. this equal to'

*ecall that marinal bene!it is∆

BO ∆

O

)()( H H B H B B ′∆−−=′∆

3%36



Slope MB

' H H ∆−

)' H H ( B ∆−

' H ∆

' ' H H ∆− H

' ' B∆

' ' H ∆

' H / ' B ∆∆

)' ' H H ( B ∆−

)H ( B

' B∆

Slope MB

Slope MB ' ' H / ' ' B ∆∆

ours 2H 4

"otalBene!it254

*elationship bet(een "otalBene!it and Marinal Bene!it 2iure 3/+4

F

E

D

3%30



*elationship bet(een "otalBene!it and Marinal Bene!it

"anents to the total bene!it !unction atthree di!!erent numbers o! hours 2H = 0. H =3. H = 74Slope o! each tanent equals the marinal

bene!it at each number o! hoursiure 2b4 sho(s the MB cur)e' note ho(

the MB )aries (ith the number o! hoursMarinal bene!it cur)e is described by the

!unction MB24 -7+%;6

3%38



*elationship bet(een "otalBene!it and Marinal Bene!it 2iure 3/74

"otalBene!it 254

ours 2H 4

6 0 8 3 + 7 -

-0+

0-68

88:6

B

2a4' "otal Bene!it

Slope MB 7:+

Slope MB +0+

Slope MB 87+

6 0 8 3 + 7 -

87+

+0+

7:+

Marinal Bene!it25hour4

MB

2b4' Marinal Bene!it

-7+

ours 2H 4

3%33



*elationship bet(een "otal Costand Marinal Cost

<arallels relationship bet(een total bene!it cur)eand marinal bene!it

When actions are !inely di)isible. the marinal

cost (hen choosin action K is equal to theslope o! the total cost cur)e at K

Gsin Calculus

3%3+

( ) ( )dHHdCHMC =



*elationship bet(een "otal Costand Marinal Cost

"anents to the total cost cur)e at threedi!!erent numbers o! hours 2H = 0. H = 3. H= 74Slope o! each tanent equals the marinal

cost at each number o! hoursiure 2b4 sho(s the MC cur)e' note ho(

the MC )aries (ith the number o! hoursMarinal cost cur)e is described by the

!unction MC24 006I;6

3%37



*elationship bet(een "otal Costand Marinal Cost 2iure 3/-4

006

096

376

706

076

-96

0776

"otal Cost254

2a4' "otal Cost 2b4' Marinal Cost

0 8 3 + 7 -

ours 2H 4

6

C

Slope MC 096

Slope MC 376

Slope MC 706

6 0 8 3 + 7 -

Marinal Cost25hour4

ours 2H 4

MC

3%3-



Gsin Calculus to !ind BestChoice

&et Bene!it "otal Bene!it "otal Cost

Ma#imi$e &et Bene!it 2&B244/

Gsin Calculus ( ) ( ) ( )

( ) ( ) ( ) ( )HMCHMBdH

HdC

dH

HdB

dH

HdC

dH

HdB

dH

HdNB

=⇒=⇒

=−= 0



Gsin Calculus to !ind BestChoice

So. at the ma#imum MB(H) = MC(H).

MB24 -7+%;6

MC24 006I;6Sol)in. (e obtain 3/+/



Marinal Bene!it Equals MarinalCost at a Best Choice

At the best choice o! 3/+ hours. the &oMarinal Fmpro)ement <rinciple holds soMB MC

At any number o! hours belo( 3/+. MB MC. so a small increase in repair time (illimpro)e the net bene!it

At any number o! hours abo)e 3/+. MC MB. so that a small decrease in repairtime (ill impro)e net bene!it

3%39



Marinal Bene!it Equals Marinal

Cost at a Best Choice 2iure 3/:4

MarinalBene!it.MarinalCost 25hour4

ours 2H 4

MC

MB

3/+

6 0 8 3 + 7 -

006

3;8

-7+

3%+6



Slopes o! "otal Bene!it and "otalCost Cur)es at the Best Choice

MC MB at the best choice o! 3/+ hourso! repair

"here!ore. the slopes o! the total bene!itand total cost cur)es must be equal atthis point

"anents to the total bene!it and totalcost cur)es sho( this relationship

3%+0



Slope o! "otal Bene!it and "otalCost Cur)es 2iure 3/;4

6 0 8 3 + 7 -

ours 2H 4

"otalBene!it"otalCost254 B

C 98+/;6

3/+

3%+8



Sunk Costs and Decision Makin

A sunk cost is a cost that the decisionmaker has already incurred. or A cost that is una)oidable reardless o!

(hat the decision maker does/Sunk costs a!!ect the total cost o! a

decision

Sunk costs do not a!!ect marinal costsSo sunk costs do not a!!ect the best choice

3%+3



Car *epair E#ample' Best Choice(ith a Sunk Cost

iure 3/9 sho(s a cost%bene!itcomparison !or t(o possible cost !unctions(ith sunk !i#ed costs' 5766 and 50066/Fn both cases. the best choice is H 3/+'

the le)el o! sunk costs has no e!!ect on thebest choice

&otice that the slopes o! the t(o total costcur)es. and thus the marinal costs. arethe same

3%++



Best Choice (ith a Sunk Cost2iure 3/94

766

ours 2H 4 3/+

6 0 8 3 + 7 -

C

C´

B

%0:7/86

+8+/;6

"otalBene!it."otal Cost254

0066

Balacing Costs and Benefits

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