ECO 642 QA - MANAGERIAL ECONOMICS

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Managerial Economics Formulas1 Elasticity of Demand

,

%

%

%

%

%

%

x x x

p

x x x

x x x

I

D

xX Y

x y

Y y x

Q dQ P E

P dP Q

Q dQ P E

I dI I

dQQ P E

P dP Q

  



  



  



Price, Marginal Revenue and Elasticity

1 1 1

1 1P

P

MR P P MR E

E

                 

Consumption Theory

X XY

Y

X X X Y

Y Y X Y

X Y

MU MRTS

MU

MU P MU MU

MU P P P

X P Y P I



  

 

Calculus Rules: Derivatives

 If , 0 dy

y a then dx

 

 If 1

, b bdY

y ax then abx dx

  

 If     , dy dy dz

y u x z x then dx dx dx

   

 If    . , then dY dZ dU

y u x z x u z dx dx dx

  

 If  

  2 . .

,

du dz z u

u x dy dx dxy then z x dx z



 

At Maximum 2

2 0

Y

X

 

 and at minimum

2

2 0

Y

X

 



Production Theory ( )

L L L

L K L L

L K K K

L K

TP d TP AP MP P MP W

L dL

MP MP MP P

P P MP P

TC L P K P

  

  

 

1 Ibrahim Elsaify, Applications in Managerial Economics, 2011. All Rights Reserved.

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Economies of Scale

( , )

( , )

Q f L K

Q f L K

Q Q IRS

 







 

Economies of Scope

, ) , 0) , )

) ) , ) , 0

, )

( ( (0

( ( (

(

x y x y

x y x y

x y

Economies of Scope

Also S Economies of Scope

TC Q Q TC Q TC Q

TC Q TC Q TC Q Q

TC Q Q

  

    

Equilibrium Conditions:

Market Equilibrium: Q Q

d s 

Firm Equilibrium: MR = MC where

( ) ( )

d TR d TC MR and MC

dQ dQ  

where TR TC TR P Q   

Cost Functions

( ) ( )

AC AVC AFC

TC TVC TFC

TC TVC TFC

Q Q Q

d TC d TVC MC

dQ dQ

 

 

 

Market Concentration a. N-Firm Concentration Ratio (N-Firm CR)

1 2 3 4 4 1 2 3 4

: i i

T T

S S S S S C W W W W Where W

S S

        

b. Herfindahal-Herchman Index (HHI)

1

2 2 2 2

10, 000 0 10, 000

1 1 1 1 1 : .....

1 -

n

i

i

HHI W where HHI

HHI N N N N N N

Number equal size firms in the market HHI





      

 

     



With N equal size firms

c. Lerner Index and Markup Factor

Markup Factor

1

1

1

1 P

E

P MC P L P MC Markup Factor

P L MC 



     



d. Rothchild Index Market Elasticity of Demand

Firm Elasticity of Demand

MK

F

RI 

 