Managerial Economics Hand note in a document For MBA

Managerial Economics Lectured by RUBA RUMMANA Asst: prof: A&S of AUST

Content

01 Lecture 3 Demand & supply 01

02 Lecture 4 Elasticity of demand and supply 12

03 Lecture 5 Theory of Utility 18

04 Lecture 6 Producer Equilibrium 23

05 Lecture 7 Theory of cost 26

06 Lecture 7B Theory of revenue 32

07 Lecture 8 Market structure 33

08 Lecture 9 Integration 44

Prepared by Khondoker Amin Uzzaman

ID: 15/02/51/002 MBA Fall-2015

School of Business AUST

1 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Managerial Economics

Demand

Lecture 3

Qd tea = ∫{𝑃𝑡𝑒𝑎, 𝑃𝑠(𝑐𝑜𝑓𝑓𝑒), 𝑃𝑐(𝑚𝑖𝑙𝑘), Y, T}

Won price cross price

Low of demand

Ceteris Paribus

Qd tea = ∫{𝑃𝑡𝑒𝑎, 𝑃𝑠(𝑐𝑜𝑓𝑓𝑒), 𝑃𝑐(𝑚𝑖𝑙𝑘), Y, T}

𝑃𝑡𝑒𝑎 𝑄𝑑𝑡𝑒𝑎

5 10

8 6.5

12 1

20 0.25

𝑃𝑡𝑒𝑎

8 A

5 B

𝑄𝑑𝑡𝑒𝑎 0 6.5 10

2 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Qd = ± a – bp

Constant value of slope slope

20-0.5p

Movement and shifting of demand curve

1. Movement along the demand curve when own price changes,

variable constant.

2. Shifting of the curve

Qd tea = ∫{𝑃𝑡𝑒𝑎, 𝑃𝑠(𝑐𝑜𝑓𝑓𝑒), 𝑃𝑐(𝑚𝑖𝑙𝑘), Y, T}

Y= 5000 tk 5 tk @ 10 kg Y= 10000 tk 5 tk @ 25 kg Y= 3000 tk 5 tk @ 5 kg

𝑃𝑡𝑒𝑎

Y

D i D D ii

0 5 10 25 Qd tea

3 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Exercise 1: Y= income

𝑃𝑡𝑒𝑎

d di

0 Qd tea

Condition: Y

Exercise 2:

𝑃𝑡𝑒𝑎

d i d

0 Qd tea

Condition: Y

4 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Exercise 3:

𝑃𝑡𝑒𝑎

di

d

0 Qd tea

Condition: Price of milk

Exercise 4:

𝑃𝑡𝑒𝑎

di

d

0 Qd tea

Condition: price of coffee

****Own price variable shifting****

5 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Supply

50 kg onion

35 tk 50 kg 50kg = mkt = ss

30 tk 50 kg 40kg = mkt = ss

𝑄𝑠𝑄𝑠 𝑆𝑠 𝑠𝑠 }

Supply

Natural Import tax subsidy

Supply function Ceteris Paribus

𝑄𝑠 𝑟𝑖𝑐𝑒 = ∫{𝑃𝑟𝑖𝑐𝑒, 𝑃𝑠(𝑤ℎ𝑒𝑎𝑡), 𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑠, N, T, S}

Price 𝑄𝑠 𝑟𝑖𝑐𝑒

Price 𝑄𝑠 𝑟𝑖𝑐𝑒

6 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

𝑃𝑟𝑖𝑐𝑒 𝑄𝑠𝑟𝑖𝑐𝑒

50 100

80 250

100 500

120 700

𝑃𝑟𝑖𝑐𝑒 s

80 50

0 100 25 𝑄𝑠𝑟𝑖𝑐𝑒

𝑄𝑠 𝑟𝑖𝑐𝑒 = ∫{𝑃𝑟𝑖𝑐𝑒, 𝑃𝑠(𝑤ℎ𝑒𝑎𝑡), 𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑠, N, T, S}

Price 𝑆𝑖 𝑆

𝑆𝑖𝑖

50

0 80 100 150 𝑄𝑠𝑟𝑖𝑐𝑒

7 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

*** i for prime

Exercise 1:

𝑃𝑟𝑖𝑐𝑒 S’

S

0 𝑄𝑟𝑖𝑐𝑒

*** Condition: factors price and own price constant

Exercise 2:

𝑃𝑟𝑖𝑐𝑒

S

S’

0 𝑄𝑟𝑖𝑐𝑒

*** Condition: subsidy’s and own price constant

8 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Exercise 3:

𝑃𝑟𝑖𝑐𝑒

S’

S

0 𝑄𝑟𝑖𝑐𝑒

*** Condition: Price of wheat and own price constant

Exercise 4:

𝑃𝑟𝑖𝑐𝑒

S’

S

0 𝑄𝑟𝑖𝑐𝑒

*** Condition: there occurs are Drought

9 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Equilibrium of Demand and Supply

P---- Qd ----- Qs ---- state of the market ----- pressure on

6---- 10 ----- 16 ----- surplus -------------- Price

4---- 12 ----- 12 ----- Equilibrium -------- Natural

2---- 16 ---- 10 ------ shortage ----------- Price

𝑃𝑟𝑖𝑐𝑒

S

Excess ss

6 4 E 2

D 𝑄𝑑𝑟𝑖𝑐𝑒 0 10 12 16

Excess D

Shift in equilibrium

10 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Case 1: 𝑃𝑟𝑖𝑐𝑒 S’

S

P’ E E’ P

D’

D

0 𝑄𝑟𝑖𝑐𝑒 Q Q’ *** Condition Y Sub Case 2 S’ 𝑃𝑟𝑖𝑐𝑒 S

E P E’ P’ D’ D

0 Q’ Q Qd

*** Condition Y T

Qd = 200

3 - 𝑝

3

QS = -20+P

Find the equilibrium P and Q

In equilibrium Qd = Qs

11 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

200

3−

𝑃

3= −20 + 𝑃

P = 65

Q = 45

Qd = 45 = Qs

P

200/3

65 E

d

-20 0

12 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Elasticity of demand and supply Lecture 4 29/01/16

𝑄𝑑𝑐𝑜𝑓𝑓𝑒𝑒 = 20 + 0.2 Ptea - 0.3 Pcoffee

∆

∆𝑃𝑐𝑜𝑓𝑓𝑒𝑒 (𝑄𝑑𝑐𝑜𝑓𝑓𝑒𝑒 ) = 0 + 0 – 1 * 0.3 𝑃𝑐𝑜𝑓𝑓𝑒𝑒

1−1

= - 0.3 𝑃𝑐𝑜𝑓𝑓𝑒𝑒0

= - 0.3

Elasticity

Demand supply

1. Own price elasticity (ɳ 𝑃𝑡𝑒𝑎)

2. Cross price elasticity (ɳ 𝑃𝑡𝑒𝑎,𝑚𝑖𝑙𝑘,𝑐𝑜𝑓𝑓𝑒𝑒)

3. Income elasticity (ɳ 𝑌)

Appendix Differentiation Costing power function rules

Qd = ∫(𝑃) 𝑄𝑑𝑡𝑒𝑎 = ∫(𝑃𝑡𝑒𝑎)

𝑄𝑑𝑡𝑒𝑎 = 20 – 0.5 Ptea ∆

∆𝑃𝑡𝑒𝑎 (Qd)= -1 * 0.5 𝑃𝑡𝑒𝑎

1−1

= -0.5 𝑃𝑡𝑒𝑎0

= -0.5

13 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

𝑃𝑡𝑒𝑎 = 5 Qtea = 10 Pcoffee = 8 Pmilk = 3 Y = 10000

𝑄𝑑𝑡𝑒𝑎 = 20 – 0.5 Ptea + 0.2 Pcoffee – 0.3 Pmilk + .0001 Y

1. Own price elasticity (ɳ 𝑷𝒕𝒆𝒂)

ɳ 𝑃𝑡𝑒𝑎 = ∆

∆𝑃𝑡𝑒𝑎 (𝑄𝑑𝑡𝑒𝑎 ) ×

𝑃𝑡𝑒𝑎

𝑄𝑑𝑡𝑒𝑎

= -0.5 × 5

10

= -0.25

= 0.25 < 1

Change in 𝑄𝑑𝑡𝑒𝑎 < change in Ptea

Comment: Tea is a necessary good

N:B = if ɳ 𝑃𝑡𝑒𝑎 > 1

Comments: Tea is a luxury good

2. Cross price elasticity (ɳ 𝑷𝒕𝒆𝒂,𝒎𝒊𝒍𝒌,𝒄𝒐𝒇𝒇𝒆𝒆)

a. 𝑄𝑑𝑡𝑒𝑎 = 20 – 0.5 Ptea + 0.2 Pcoffee – 0.3 Pmilk + .0001 Y

ɳ 𝑃𝑡𝑒𝑎,𝑐𝑜𝑓𝑓𝑒𝑒 = ∆

∆𝑃𝑐𝑜𝑓𝑓𝑒𝑒 (𝑄𝑑𝑡𝑒𝑎 ) ×

𝑃𝑐𝑜𝑓𝑓𝑒𝑒

𝑄𝑑𝑡𝑒𝑎

= 0.2 × 8

10

= 0.16

Comments: Tea and Coffee are substitutes

N:B = if ɳ 𝑃𝑡𝑒𝑎,𝑐𝑜𝑓𝑓𝑒𝑒 = (+1)

Comments: Tea and Coffee are perfect substitutes

b. ɳ 𝑃𝑡𝑒𝑎𝑚𝑖𝑙𝑘 = ∆

∆𝑃𝑚𝑖𝑙𝑘 (𝑄𝑑𝑡𝑒𝑎 ) ×

𝑃𝑚𝑖𝑙𝑘

𝑄𝑑𝑡𝑒𝑎

= - 0.3 × 3

10

= - 0.9

Comments: Tea and milk are complement

14 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

𝑃𝑡𝑒𝑎 = 5 Qtea = 10 Pcoffee = 8 Pmilk = 3 Y = 10000

N:B = if ɳ 𝑃𝑡𝑒𝑎𝑚𝑖𝑙𝑘 = (-1)

Comments: Tea and Milk are perfect complements

3. Income elasticity (ɳ 𝒀)

(ɳ 𝒀) = ∆

∆𝑌 (𝑄𝑑𝑡𝑒𝑎) ×

𝑌

𝑄𝑑𝑡𝑒𝑎

= 0.0001 × 10000

10

= 0.1

Comments: Tea is a normal good

N:B = if (ɳ 𝒀) = (-) negative

Comments: Tea is an inferior good

Question: Drive the function for coffee when…..

I. It is luxury.

II. It has one perfect substitutes

III. It has one perfect complements

IV. It is a normal good

I. Luxury = own price elasticity > 1

II. Cross elasticity +1 price substitutes

III. Cross elasticity -1 price complement

IV. Normal good = income elasticity

𝑸𝒅𝒄𝒐𝒇𝒇𝒆𝒆 = 20 – 4 Pcoffee + 1.25 Ptea – 3.3 Pmilk

I. ɳ 𝑷𝒄𝒐𝒇𝒇𝒆𝒆 = ∆

∆𝑷𝒄𝒐𝒇𝒇𝒆𝒆 (𝑸𝒅𝒄𝒐𝒇𝒇𝒆𝒆 ) ×

𝑷𝒄𝒐𝒇𝒇𝒆𝒆

𝑸𝒅𝒄𝒐𝒇𝒇𝒆𝒆

= - 4 × 5

10

= - 2

15 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

= 2 > 1

Comment: coffee is a luxury good

II. ɳ 𝑷𝒕𝒆𝒂,𝒄𝒐𝒇𝒇𝒆𝒆 = ∆

∆𝑷𝒕𝒆𝒂 (𝑸𝒅𝒄𝒐𝒇𝒇𝒆𝒆 ) ×

𝑷𝒕𝒆𝒂

𝑸𝒅𝒄𝒐𝒇𝒇𝒆𝒆

= 0.25 × 8

10

= 1

Comment: Coffee has one perfect substitutes

III. ɳ 𝑷𝒄𝒐𝒇𝒇𝒆𝒆,𝒎𝒊𝒍𝒌 = ∆

∆𝑷𝒎𝒊𝒍𝒌 (𝑸𝒅𝒄𝒐𝒇𝒇𝒆𝒆 ) ×

𝑷𝒎𝒊𝒍𝒌

𝑸𝒅𝒄𝒐𝒇𝒇𝒆𝒆

= - 3.3 × 3

10

= -1

Comment: Coffee has perfect complement

IV. (ɳ𝑷𝒄𝒐𝒇𝒇𝒆𝒆 𝒀) = ∆

∆𝒀 (𝑸𝒅𝒄𝒐𝒇𝒇𝒆𝒆) ×

𝒀

𝑸𝒅𝒕𝒆𝒂

= 0.0001 × 10000

10

= 0.1

Comments: Coffee is normal good

16 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Lecture 4 extend

Elasticity of a straight line demand curve using point elasticity formula =

𝒆𝒑𝒐𝒊𝒏𝒕 = 𝒍𝒐𝒘𝒆𝒓 𝒍𝒆𝒈𝒎𝒆𝒏𝒕

𝒖𝒑𝒑𝒆𝒓 𝒔𝒆𝒈𝒎𝒆𝒏𝒕

P 4 A (Perfect Elastic Region) 3 B (Elastic Region) 2 M (Unit Elastic Region) 1 D (Inelastic Region) R (Perfect Inelastic Region) 0 1 2 3 4 Q

𝑒𝑀 = 2

2 = 1 = e = 1

𝑒𝐵 = 3

1 = 3 = e > 1

𝑒𝐷 = 1

3 = 0.33 = e < 1

𝑒𝐴 = 4

0 = ∞ = e = ∞

𝑒𝑅 = 0

4 = 0 = e = 0

17 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Elasticity of supply

𝒏𝑷𝑸𝒔𝒕𝒆𝒂 =

∆

∆𝒑𝒕𝒆𝒂 (𝑸𝒔𝒕𝒆𝒂) ×

𝑷𝒕𝒆𝒂

𝑸𝒔𝒕𝒆𝒂

= (+) ve

P es = 1

es = ∞

0 es = 0 Q

18 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Lecture 5 Theory of Utility

Utility measurement is the primary steps for demand creation.

Measurement of utility

Cardinal Ordinal Money

Tools -------{1. 𝑇𝑜𝑡𝑎𝑙 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 (𝑇𝑈)

2.𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 (𝑀𝑈)

Units of consumption ------- TU --------- MU (Example of Mango ) 0 --------- 0 ------- 0 1st --------- 4 -------- 4 2nd --------- 7 -------- 3

3rd --------- 9 -------- 2 (Extra ) 4th --------- 10 -------- 1 5th --------- 10 -------- 0 6th --------- 8 -------- -2 Law of diminishing MU (increasing at a decreasing rate) MU

0 Q

19 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Consumer equilibrium condition under cardinal management =

Equal MU for every good = 𝑀𝑈𝑥

𝑃𝑥 =

𝑀𝑈𝑦

𝑃𝑦 =

𝑀𝑈𝑧

𝑃𝑧 = ………. 𝜆 (constant utility of money)

𝑀𝑈𝐵 > 𝑀𝑈𝐶 Units of consumption ------- TU --------- MU (Example of Apple) 0 --------- 0 ------- 0 1st --------- 5 -------- 5 2nd --------- 9 -------- 4 3rd --------- 13 -------- 3 4th --------- 14 -------- 1 5th --------- 14 -------- 0 6th --------- 12 -------- -2 Ordinal Management

Tools {1. 𝐼𝑛𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑐𝑢𝑟𝑣𝑒 (𝑖𝑒)

2. 𝐵𝑢𝑑𝑔𝑒𝑡 𝑙𝑖𝑛𝑒

1. Indifference Curve Possibilities ------- x ------- y ------- Utility ------- State of the consumer A ------- 5 ------- 1 ------- U0 ------- Indifference B ------- 4 ------- 2 ------- U0 ------- Indifference C ------- 3 ------- 3 ------- U0 ------- Indifference D ------- 2 ------- 2 ------- U0 ------- Indifference y

a

b c d IC2=U1

IC1=U0

0 X

A

B C D

20 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Assumption:

I. x,y are completely substitutable

II. consumer always prefects more to less

III.

Slope of IC = ∆𝑦

∆𝑥 = Marginal rate of substitution = MRSx,y =

𝑀𝑈𝑥

𝑀𝑦

Characteristic of ICs

(i) ICs are downward

(ii) Higher ICs indicate higher utility

(iii) Two ICs Will never interests

y

U2

U1

0 z

U1 A =B

U2 B= C

A ≠ C

A

B

C

21 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

(iv) ICs are convex to the origin

y

IC1

0 x

2. Budget line (BL)

M= Px . x + Px . y

100 = 5 × 10 + 10.5

100 = 100

If x=0

= M= P.x + Py.y

=Px 0 + Py.y

∴ M= Py . y

Y = 𝑀

𝑃𝑦

If y = 0 => M = Px. X + Py. Y

M= Px. X + Py . 0

X= 𝑀

𝑃𝑥

22 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

y

A

M/Py

B

IC3

IC2

B IC1

0 M/Px x

Slope of Ab (Budget line)

∆𝑦

∆𝑥 =

𝑀𝑃𝑦𝑀𝑃𝑥

= 𝑀

𝑃𝑦 ×

𝑃𝑥

𝑀

=𝑃𝑥

𝑃𝑦 (Price ratio)

B

𝑀𝑈𝑥

𝑀𝑈𝑦 =

𝑃𝑥

𝑃𝑦

= 𝑀𝑈𝑥

𝑃𝑥 = 𝑀𝑈𝑦

𝑃𝑦

Therefore both cardinal and ordinal approaches lead to the same conclusion about

consumer equilibrium.

Write down the demand function for the business manager

(By the employer)

23 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

𝑄𝑑𝐵𝑀 =

∫{𝑠𝑎𝑙𝑎𝑟𝑦𝐵𝑀 , 𝑠𝑎𝑙𝑎𝑟𝑦𝐷𝑖𝑝, 𝑃𝑐(𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑟 𝑖𝑛𝑡𝑒𝑟𝑛𝑒𝑡,𝑀𝑜𝑏𝑖𝑙𝑒, 𝑒𝑡𝑐), 𝑦(𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑟)𝑇 }

Lecture 6

Producer Equilibrium 04/03/2016

1. ISO quant/ ISO product (IQ)

2. ISO – Cost

1.ISO quant/ ISO product (IQ)

Possibilities ---------- L ----------A ------- Production ---------- State of the producer

A ---------- 5 --------- 1 ------- Q0 ----------- indifference

B ---------- 4 --------- 2 ------- Q0 ----------- indifference

C ---------- 3 --------- 3 ------- Q0 ----------- indifference

D ---------- 3 --------- 3 ------- Q0 ----------- indifference

L

A

IQ2= Q2

B IQ1= Q1

C D IQ = Q0

0 A

24 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Marginal rate of technical substitution

Slope of IQ = MRTSL,A = 𝑑𝐴

𝑑𝐿 =

𝑀𝑃𝐿

𝑀𝑃𝐴

Characteristics of IQ

(i) IQs are downward

(ii) Higher IQs indicated higher production

(iii) Two IQs will never intersect

Q1 => A = B

Q2 => B = C

A=C

A

A C Q2

B Q1

0 L

2.. ISO – cost

M = PL . L +PA . A

=4.10 +10.6

∴ 100 = 100

25 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

L = 0

M = PL . L +PA . A

= PLO +PA . A

=PA A

A= 𝑀

𝑃𝐴

A

𝑀

𝑃𝐴 A

B

0 𝑀

𝑃𝐿 L

Slope of AB = 𝑑𝐴

𝑑𝐿 =

𝑀𝑃𝐴𝑀𝑃𝐿

= 𝑃𝐿

𝑃𝐴 = price ratio

A

A

B Q3

Q2

Q1

0 L

26 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

B

𝑀𝑃𝐿

𝑀𝑃𝐴 =

𝑃𝐿

𝑃𝐴

𝑀𝑃𝐿

𝑃𝐿 =

𝑀𝑃𝐿

𝑃𝐴

Production equilibrium

Lecture 7 Theory of cost

1. Land = L = rent = r

2. Labor = A = wages = w

3. Capital = K = interest = i

4. Organization = o = profit = 𝜋

Cost of producing Q = r+w+i+ 𝜋

“Profit is the prize of risk bearing”

Types of cost

1. Total cost = total fixed cost + total variable cost

TC = TFC + TVC

2. Average cost = AC = 𝑇𝐶

𝑄 =

𝑇𝐹𝐶+𝑇𝑉𝐶

𝑄

AC = AFC +AVC

3. Marginal cost = MC = 𝑑

𝑑𝑄 (TC)

10------100

11------ 150

MC= 50

27 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Units of production ------- TC ------- MC

0 ------ 55

30

1st ------ 85

25

2nd ------ 110

20

3rd ------ 130

30

4th ------ 160

50

5th ------ 210

MC 50 ‘U’ shaped MC

30

20

0 Q

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Short Run cost curve

Cost MC AC AVC

AFC

0 Q

Minimum AC (AC=MC)

AC

MC MC AC

0 A B C Q

Production

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Q. What dose minimum AC imply

producer out put

4

A

AC > MC

AC = 4+4+4+4

4 = 4

AC = 4+4+4+4+5

5 = 4.20

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Long run cost curve

Cost

LAC

SMC1 SAC1 SMC2 SAC2 SMC3 SAC3

0 Q1 Q’1 Q2 Q3

Other name of LAC = Long Run Envelope Curve

LAC’ LMC

0 Q* Q

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*Draw the LAC From Five plant size

Cost

LAC

SMC1 SAC1 SMC2 SAC2 SMC3 SAC3 SMC4 SAC4 SMC5 SAC5

0 Q1 Q’1 Q2 Q3 Q4 Q5

i. Given

IC = 5Q3 + 2Q2 + 13Q +7

Find AC and MC

∴ AC = TC = 5𝑄3 + 2𝑄2 + 13𝑄 +7

𝑄

= 5Q2 + 2Q + 13 +7/Q

∴ MC = 𝑑

𝑑𝑄 (TC) = 15Q2 + 4Q + 13

ii. Given ,

AC = 5Q2 + 30Q + 5/Q

Find MC

IC = AC × Q

= (5Q2 + 30Q + 5/Q) × Q

=5Q3 + 30Q2 + 5

MC = MC = d/dQ (TC) = 45Q2 + 60

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Lecture 7 B

Theory of revenue

1. Revenue = R = total revenue = TR = P× Q

= 5 × 10

= 50

2. Average revenue AR = 𝐼𝑅

𝑄 = 𝑃×𝑄

𝑄 = P

3. Marginal revenue MR = 𝑑

𝑑𝑄 (TR)

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Lecture 8 Market structure / 11.03.2016

Note:

3.1 Pure / Perfect

Assumption

a) Larger number of buyer and seller b) Homogenies product sold

Classcification

1. Time

Temporary

Parmanent

2. Durability

Temporary

Parmanent

3. Compitition

(দর কষা কষষ ও সুয াগ এর ষিষিযে Compitition ২ প্রকার)

3.1 Pure / Perfect

3.2 Imperfect

Most important roll of classification

34 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

c) Perfect knowledge about the market d) No bar for entry and exit

3.1 (a) DD curve for a firm in the short run P

P=d= AR

0 Q

(b) Break even condition for firm in short run (P=MC)

P MC AC

B 40 P=d=AR

0 4 Q

B

𝜋 = TR – TC

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TR = P × Q = 40 × 4 = 160

TC = AC × Q = 40 × 4 = 160

𝜋 = 0

(Normal Profit) [𝐴 =

𝑇𝐶

𝑄

∴ 𝑇𝐶 = 𝐴𝐶 × 𝑄]

d = s => P/

P = MC <= P/Q

3.2 Imperfect

Imperfect

a. Mono poly

(single seller)

b. Oligo poly

(Few Seller)

Slightly differentiated

ষিযে business করযে

c. Monopolistic Compitition

( either Homogenies/ slightly defferentiated )

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3.2 . a Monopoly

World

i. Price – output determination

Under natural monopoly (MC = MR)

P

0 M

𝜋 = TR – TC

TR = P × Q = QP1 × 0M = 0P1 GM

TC = AC × Q = 0W × 0M = 0WFM

𝜋 = P1GFW > 0 [𝑆𝑢𝑝𝑝𝑒𝑟 𝑛𝑜𝑟𝑚𝑎𝑙 𝑝𝑟𝑜𝑓𝑖𝑡 ]

MR P=d=AR Q

P1

W

G

F

MC AC Note:

p

0 Q

00

10

MR

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3.2.a

ii. Area of operation of natural Monopoly

*When MC > 0 ( )

P

e> 1

C e = 1 (MR= 0)

e<1 (MR < 0)

0 P=d=AR Q

MR = 𝑑

𝑑𝑄 (TR)

= 𝑑

𝑑𝑄 (P× Q)

= 𝑑

𝑑𝑄 {(−𝑀𝑄 + 𝐶)𝑄}

= 𝑑

𝑑𝑄 (- MQ2 + CQ)

MR = -2 MQ +C

P= AR = -MQ +C

e = 1 => AR = 𝑐

2

C - 𝑐

2 = MQ

MQ = 2𝐶−𝐶

2

∴ MQ = 𝐶

2

38 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Iff = if an only if

Iff MC > 0, The natural monopoly will operate in the elastic region (e> 1) of its demnd

curve

**When MC = 0

P

e> 1

e = 1

e<1

E(MC=MR)

0 MR P=d=AR Q

Iff MC = 0, Unit elastic region (e=1)

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Lecture 8 extend 13.03.2016

In perfect competition

3.1 Perfect competition

3.1. b) Shut down point

P MC AC AVC

Pd M

Pd1 M’ 0 Q

M= Breakeven point MC = P

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3.2.C) Monopolistic Competition

3.2.C. i) Short Run Super Normal Profit of a firm (MC=MR)

P MC

AC

P1 G W F

E=(MC+MR)

0 M MR P=d=AR Q

TR= OP1 GM

TC=OWFM

𝜋 = P1GFW > 0

(Super normal profit)

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3.2.C. ii) Short run loss (MC=MR)

MC

P

AC

T1 T’

P1 G

E=(MC+MR)

0 M MR P=d=AR Q

TR = P×Q = OP1 × OM

= OP1OM

TC= AC × Q = OT1 × OM

= OT1T’M

Loss = P1T1T’G

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3.2.C iii) Long run Normal profit (𝑴𝑪 = 𝑴𝑹𝑨𝑪 = 𝑨𝑹

)

P AC

MC

P1 P’

E=(MC+MR)

0 M MR P=d=AR Q

TR = P × Q = OP1× OM

= OP1P’M

TC = AC × = OP1P’M

𝜋 = 0 (Normal profit)

P MR

MC MC=MR=> P’ P AC

P’

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3.2.2) Public utility regulation of a natural Monopoly

MC

P

AC

Pm M

PR R

Pc E(MC=MR)

MR P=d=AR

Qm QR QC Q

1. Natural monopoly P and Q = Pm and Qm => MC = MR

2. Regulated monopoly = P and Q = PR and QR => P = AC

3. Competitive P and Q = Pc and Qc = P = Mc

44 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

Integration 18/03/2016

Pd = (Q-1

∫𝑄𝑛𝑑𝑄 = ∫(𝑄 − 1)𝑑𝑄

= 𝑄𝑛+1

𝑛+1 = ∫(𝑄)𝑑𝑄 - ∫1𝑑𝑄

= 𝑄1+1

1+1 – Q

= 𝑄2

2 - Q

i. Consumer supply (CS)

Pd = (Q-1)2 when P0 = 4

Q0 = 6

Find CS,

CS = ∫ (𝑄 − 1)2𝑑𝑄 − 𝑝0𝑄0

0 𝑄0

=∫ (𝑄2 − 2𝑄 + 1)𝑄0

0 dQ - 𝑝0 𝑄0

=∫ (𝑄)2𝑑𝑄 − 2𝑄0

0 ∫ (𝑄)𝑑𝑄 + 1

𝑄0

0 ∫ (𝑄)𝑑𝑄 − 𝑃0

𝑄0

0𝑄0

= [𝑄3

3− 𝑄2 + 𝑄]

𝑄0 - 𝑝0 𝑄0

= 63

3− 62 + 6 – (6×4)

=6 ×6 ×6

3 – 36 + 6-24

=78-60

= 18

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ii. Produces surplus (PS)

PS = (Q+1)2 when P0 = 120

Q0 = 6

Find PS

PS = 𝑝0 𝑄0 - ∫ (𝑄 + 1)2 𝑑𝑄𝑄0

0

= 𝑝0 𝑄0 - ∫ (𝑄2 + 2𝑄 + 1) 𝑑𝑄𝑄0

0

= 𝑝0 𝑄0 - ∫ 𝑄2 𝑑𝑄 + 2𝑄0

0 ∫ (𝑄) 𝑑𝑄 + 1

𝑄0

0 ∫ 𝑑𝑄

𝑄0

0

=𝑝0 𝑄0 - [𝑄2+1

2+1+ 2

𝑄1+1

2+ 𝑄]

𝑄0

= 𝑝0 𝑄0 - [𝑄3

3+ 2

𝑄2

2+ 𝑄]

0

𝑄0

= 120 × 6 - [63

3+ 66 + 6]

0

6

=720 - [216

3+ 36 + 6]

0

6

= 720 - [72 + 42]06

=720 - [114]06

46 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

iii. Monopoly sell two goods x and y whose demand function are:

x = 25 – 0.5 Px

y = 30 – Py

And the combined cost function is C = x2 + 2xy + y2 + 20

(a) Profit maximizing level of output for x and y

(b) Profit maximizing level of output for (Px , Py)

(c) Maximum profit

(a) Profit maximizing level of output for x and y

𝜋 = TR –TC

= TRx + Try – TC

= (Px . X) + (Py . Y) – TC

={(50-2x)x + (30-y) y} – TC

= 50x – 2x2 + 30y – 42 – 2xy – y2 – 20

𝜋xy= 50x – 3x2 + 30y – 2y2 – 2xy – 20

𝜋xx= 50 – 6x – 2y = 0 (× 𝟑)

𝜋yy = 30 – 2x – 4y = 0 (× 𝟑)

50 – 6x – 2y = 0 30 – 2x – 4y = 0

- + + 10y=40

Y= 4

X= 7

Side note:

X= 25-0.5 Px

0.5Px = 25-x

Px = 25−𝑥

0.5

Px = 50 – 2x

Y = 30-Py

Py= 30-y

47 | p r i n c e . p i r o n 0 1 6 7 3 0 0 9 8 4 6

(b) Px= 50-2x= 36

Py = 26

(c) πxy= 50x – 3x2 + 30y – 2y2 – 2xy – 20

iv. The MC of manufacturing x good is 6+10x-6z2. If the TC of producing of

function of good is 12. Find TC and AC

TC = 6x +10 𝑥2

2 – 6

𝑥3

3 +K [K = constant of integration]

X=2 then TC = 12

12 = 6 . 2 + 10 22

2 – 6

23

2 + K

K = 12 -12 – 20 + 16

K = - 4

TC = 6x + 10 𝑥2

2 - 6𝑥2

2 - 6𝑥3

3 – 4

AC = 𝑇𝐶

𝑥 = 6 + 5x – 2x2 -

4

𝑥