Managerial Economics Hand note in a document For MBA
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Transcript of 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
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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
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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
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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
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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
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(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