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Managerial EconomicsAce Institute of Management
Executive MBA Program
Remainings from Objectives of the Firm
InstructorSandeep Basnyat
[email protected] 892281
Profit Maximization
• If increase Q by one unit,revenue rises by MR,cost rises by MC.
• If MR > MC, then increase Q to raise profit. • If MR < MC, then reduce Q to raise profit. • What Q maximizes the firm’s profit?
Profit Maximization
505
404
303
202
101
45
33
23
15
9
$5$00
Profit = MR – MC
MCMRProfitTCTRQAt any Q with MR > MC,
increasing Q raises profit.
5
7
7
5
1
–$5
10
10
10
10
–2
0
2
4
$6
12
10
8
6
$4$10
At any Q with MR < MC,
reducing Q raises profit.
Firms maximize profit by producing the Quantity until MR = MC
Exercise Assume a cost function: TC = 1000 + 2Q + 0.01Q2 and a constant marginal revenue $10 per unit for a firm.a) Calculate the profit maximizing output (Q); and b) Total profit if the selling price per unit (P) = MR.
Solution:a) MC = dTC /dQ = 2+0.02QProfit maximizing output is at where MR = MC10 = 2+0.02QTherefore, Profit Maximizing Quantity (Q) = 400 units.
b) Profit = TR –TC = [(PxQ) – TC] = [(10x400) – (1000 + 2(400) + 0.01(4002)] = $600
ExerciseAssume the following functions for a firmDemand : Q = 90 – 2PTotal Revenue: TC = Q3 - 8Q2 + 57Q + 2Find the followings for this firm.
a)Profit maximizing Quantityb)Price per unitc) Total Profit
Q = 4P = 43π = 6
1.506
2.005
2.504
3.003
3.502
1.50
2.00
2.50
3.00
3.50
$4.004.001
n.a.
9
10
10
9
7
4
$ 0$4.500
MRARTRPQ
–1
0
1
2
3
$4
Sales Revenue or Revenue Maximization
Sales Revenue
Maximization Condition
MR = 0
ExerciseAssume the following functions for a firmDemand : P = 7,500 – 3.75QTotal Cost: TC = 1,012,500 + 1,500Q + 1.25Q2
Find the followings for this firm.
Q = 1000 units.a)Revenue maximizing Quantityb)Price per unitc) Total Revenued)Total Profit / Loss
P = 3,750TR = 3,750,000π = - 12,500
ExerciseAssume the following functions for a firmDemand : P = 4,000 – 20QTotal Cost: TC = 2000 + 400QFind the followings for this firm under (a) Profit maximization objective(b) Revenue Maximization objective.
i) Maximizing Quantityii) Price per unitiii) Total Profit / Loss
Profit Revenue90 1002200 20001,60,000 1,58,000
Numerical ExerciseAssume the following functions for a firm:Demand : P = 20 – QTotal Cost: TC = Q2 + 8Q + 2a) Find Price (P), Quantity (Q) and Total Profit (or
Loss) for each of the following conditions:i) Profit maximizationii) Revenue Maximizationb) Find Price (P), Quantity (Q), Total Revenue (TR)
and Total cost (TC) for sales maximization with profit constraint or profit constraint of 8 or higher.
P = 17, Q = 3, π = 16
P = 10, Q = 10, π = 82 (loss)
When Q = 1; P = 19, TR = 19, TC = 11When Q = 5; P = 15, TR = 75, TC = 67Firm should produce Q = 5.
Average Total Cost or Average Cost Minimization
• Related to two important costs: MC and ATCRecall:
ATC = AFC + AVC or TC / Q
MC = ∆TC∆Q
Marginal Cost (MC) is the change in total cost from producing one more unit:
Marginal Cost
6207
4806
3805
3104
2603
2202
1701
$1000
MCTCQ
140
100
70
50
40
50
$70∆TC∆Q
MC =
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Costs
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Cost
s
Average Total Cost Curves
88.57
80
76
77.50
86.67
110
$170
n.a.
ATC
6207
4806
3805
3104
2603
2202
1701
$1000
TCQ
Important Economic Relation: ATC and MC
ATCMC
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Cost
s
When MC < ATC,ATC is falling.
When MC > ATC,ATC is rising.
The MC curve crosses the ATC curve at the ATC curve’s minimum.
ATC is minimum where,
ATC = MCAVC is minimum where,
AVC = MC
ExerciseGiven the cost function:
TC = 1000 + 10Q - 0.9Q2 + 0.04Q3
Find Q when AVC is minimum.
SolutionWhen AVC is minimum:
AVC = MC 10 - 0.9Q + 0.04Q2 = 10-1.8Q+ 0.12Q2
Or, - 0.08Q2 + 0.9Q = 0Or, Q(- 0.08Q+ 0.9) = 0Or, Q =0 and - 0.08Q+ 0.9 = 0 i.e, Q = 11.25 (Minimum AVC)
ExerciseAssume the following functions for a firmDemand : P = 7,500 – 3.75QTotal Cost: TC = 1,012,500 + 1,500Q +
1.25Q2
Find the followings for this firm if your objective is to minimize average cost.a) Q
b) Price per unitc) Total Revenued) Total Profit
P = 4,125TR = 3,712,500π = 337,500
Q = 900
Managerial EconomicsAce Institute of Management
Executive MBA Program
Session 2: Supply, Demand and Elasticity
InstructorSandeep Basnyat
[email protected] 892281
Demand• Demand comes from the behavior of buyers. • The quantity demanded of any good is the
amount of the good that buyers are willing and able to purchase.
• Law of demand: the claim that the quantity demanded of a good falls when the price of the good rises, other things equal.
$0.00
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
0 5 10 15 20 25
P
Q
The Market Demand Curve for Orange
PQd
(Market)
$0.00 24
1.00 21
2.00 18
3.00 15
4.00 12
5.00 9
6.00 6
Demand Curve Shifters: Non-price Determinants of Demand
1. Number of buyers2. Income level
a. Effect on normal goodsb. Effect on inferior good
3. Prices of other goodsa. Substitute goodsb. Complement goods
4. Taste or Preference5. Expectation
Price
QtyPrice
Qty
The ABC Marketing consulting firm found that a particular brand of portable stereo has the following demand curve for a certain region:
Q = 10,000 – 200 P + 0.03POp + 0.6I + 0.2 AWhere,Q = quantity per monthP = Price in $Pop = PopulationI = Disposable incomeA = Advertising expenditure in $a) Determine the demand curve for the company in a market in
which P = 300, Pop = 1,000,000, I = 30,000, and A = 15000
b) Calculate the quantity demanded at prices of $200
c) Calculate the price necessary to sell 45,000 units.
Numerical exercise
(Ans.: Q = 61,000 – 200P)(Ans.: 21000)
(Ans.: $80)
Supply
• Supply comes from the behavior of sellers. • The quantity supplied of any good is the
amount that sellers are willing and able to sell. • Law of supply: the claim that the quantity
supplied of a good rises when the price of the good rises, other things equal
$0.00
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
0 5 10 15
Market Supply Schedule & CurvePrice
of lattes
Quantity of lattes supplied
$0.00 0
1.00 3
2.00 6
3.00 9
4.00 12
5.00 15
6.00 18
P
Q
Supply Curve Shifters
1. Number of sellers2. Input prices3. Technology4. Expectation
Shift supply curve left or
right
$0.00
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
0 5 10 15 20 25 30 35
P
Q
Supply and Demand Together
D S Equilibrium Price and Quantity
Numerical Problem on Demand and Supply
1) Suppose:Demand eqn. for a product: Qd = 286 − 20p
Supply eqn. For a product: Qs = 88 + 40p• Find Equilibrium Quantity and Price:
Solution: Qd = Qs
286 − 20p = 88 + 40p60p = 198P = $3.30Q = 286 – 20(3.3) = 220
Comparative Static Analysis• Sensitivity analysis or “what-if” analysis.• The role of factors influencing demand is analyzed
while holding supply conditions constant. • Or, the role of factors influencing supply is
analyzed by studying changes in supply while holding demand conditions constant
• Short and Long run analyses• Short: Price adjustment to stabilize equilibrium• Long: Reallocation of resources
$0.00
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
0 5 10 15 20 25 30 35
P
Q
D S
Surplus:when quantity supplied is greater than quantity demanded
Surplus Example: If P = $5,
then QD = 9
and QS = 25
resulting in a surplus of 16 units
$0.00
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
0 5 10 15 20 25 30 35
P
Q
D S Facing a surplus, sellers try to increase sales by cutting the price.
This causes QD to rise
Surplus
…which reduces the surplus.
and QS to fall…
Short-run market change: Rationing Mechanism of Price: Surplus case
$0.00
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
0 5 10 15 20 25 30 35
P
Q
D S Facing a surplus, sellers try to increase sales by cutting the price.
Falling prices cause QD to rise and QS to fall.
Surplus
Prices continue to fall until market reaches equilibrium.
Short-run market change: Rationing Mechanism of Price: Surplus case
$0.00
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
0 5 10 15 20 25 30 35
P
Q
D S Example: If P = $1,
then QD = 21 lattesand QS = 5 lattesresulting in a shortage of 16 lattes
Shortage
Shortage
What happens if the market price is lower than equilibrium price?
$0.00
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
0 5 10 15 20 25 30 35
P
Q
D S Facing a shortage, sellers raise the price,
causing QD to fall
…which reduces the shortage.
and QS to rise,
Shortage
Short-run market change: Rationing Mechanism of Price: Shortage case
$0.00
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
0 5 10 15 20 25 30 35
P
Q
D S
Facing a shortage, sellers raise the price,
causing QD to falland QS to rise.
Shortage
Prices continue to rise until market reaches equilibrium.
Short-run market change: Rationing Mechanism of Price: Shortage case
Rationing Mechanism: Price adjustment to balance demand and supply in market
Long run analysis: Guiding or Allocating Mechanism: Market for Hybrid Cars
P
QD1
S1
P1
Q1
S2
D2
P3
Q3
EVENTS: 1. Price of gas rises2.New technology reduces production costs P2
Q2
Short-run Analysis
Long-run Analysis
Increase in D> Increase in S. What about others?
P
Q
D1
S1
P1
Q1
S2
D2
P3
Q3
P2
Q2
P
QD1
S1
P1
Q1
S2
D2
P2
Q2
Elasticity and its application
Price Elasticity of Demand
• Price elasticity of demand measures how much Qd responds to a change in P.
Price elasticity of demand =
Percentage change in Qd
Percentage change in P
Price Elasticity of Demand
Price elasticity of demand equals
P
Q
D
Q2
P2
P1
Q1
P rises by 10%
Q falls by 15%
15%10%
= 1.5
Price elasticity of demand =
Percentage change in Qd
Percentage change in P
Example:
What does elasticity = 1.5 mean?
Calculating Percentage Changes
P
Q
D
2500
10
B
2000
15
A
Calculate Price Elasticity of
Demand
Standard method of computing the percentage (%) change:
end value – start valuestart value
x 100%
Calculating Percentage Changes
P
Q
D
2500
10
B
2000
15
A
Demand for your guiding
Problem:
From A to B, P rises 25%, Q falls 33.33%,elasticity = 33.33/25 = -1.33
From B to A, P falls 20%, Q rises 50%, elasticity = 50/20 = - 2.50
How to solve this confusion?
Calculating Percentage Changes• So, we instead use the midpoint method:
end value – start valuemidpoint
x 100%
The midpoint is the number halfway between the start & end values, also the average of those values.
It doesn’t matter which value you use as the “start” and which as the “end” – you get the same answer either way!
What is PED using midpoint method?
Calculating Percentage Changes• Using the midpoint method, the % change
in P equals
2500 – 20002250
x 100% = 22.2%
The % change in Q equals
10 – 1512.5
x 100% = - 40.0%
The price elasticity of demand equals
40/22.2 = - 1.8
A C T I V E L E A R N I N G 1: Calculate an elasticity
Use the following information to calculate the price elasticity of demand for hotel rooms using midpoint method:
if P = $70, Qd = 5000
if P = $90, Qd = 3000
42
A C T I V E L E A R N I N G 1: Answers
Use midpoint method to calculate % change in Qd
(5000 – 3000)/4000 = 50%
% change in P
($70 – $90)/$80 = - 25%
The price elasticity of demand equals
43
50%25%
= - 2.0
Calculating Price Elasticity of Demand
Q
p
p
Q
pp
p
Q
%
%
Numerical example
• Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows:Price($) Demand (millions)
60 2280 20100 18120 16
Calculate the price elasticity of demand when the price is $80.
Solution to Numerical example
.P
Q
Q
P
P
PQ
Q
E D
D
D
D
D
From the above question, with each price increase of $20, the quantity demanded decreases by 2. Therefore,
QD
P
2
20 0.1.
At P = 80, quantity demanded equals 20 and
ED 80
20
0.1 0.40.
Calculating Price Elasticity of Demand
The estimated linear demand function for pork is:Q = 286 -20p
◦where Q is the quantity of pork demanded in million kg per year and p is the price of pork in $ per year.
◦ At the equilibrium point of p = $3.30 and Q = 220 Find the elasticity of demand for pork:
)/(Q
pdPdQ
Q
p
p
Q
Calculating Price Elasticity of Demand
The estimated linear demand function for pork is:Q = 286 -20p
◦where Q is the quantity of pork demanded in million kg per year and p is the price of pork in $ per year.
◦ At the equilibrium point of p = $3.30 and Q = 220 the elasticity of demand for pork:
3.0220
30.320)/(
Q
pdPdQ
Numerical Example
Demand for a publisher’s book is given as:Qx = 12,000 – 5,000Px + 5I + 500Pc
• Px = Price of the book = $5• I = Income per capita = $10,000• Pc = Price of the books from competing
publishers = $6Find Price elasticity of demand for the book.
Solution to Numerical Example
Solution:a) Substituting the values of I and Pc
Qx = 12,000 – 5,000Px + 5(10000) + 500(6)Or, Qx = 65,000 – 5,000Px
When Px = $5 (given), Qx = 40,000Now, dQx/dPx = - 5000Therefore, E p = -5000 x (5 / 40000) = - 0.625
The Determinants of Price Elasticity
The price elasticity of demand depends on: the extent to which close substitutes are
available whether the good is a necessity or a luxury how broadly or narrowly the good is defined the time horizon: elasticity is higher in the long
run than the short run.
The price elasticity of demand depends on: the extent to which close substitutes are
available whether the good is a necessity or a luxury how broadly or narrowly the good is defined the time horizon: elasticity is higher in the long
run than the short run.
The Variety of Demand Curves• Economists classify demand curves according to
their elasticity.
• The price elasticity of demand is closely related to the slope of the demand curve.
• Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity.
• The next 5 slides present the different classifications, from least to most elastic.
Q1
P1
D
“Perfectly inelastic demand” (one extreme case)
P
Q
P2
P falls by 10%
Q changes by 0%
0%
10%= 0Price elasticity
of demand =% change in Q
% change in P=
Consumers’ price sensitivity:
D curve:
Elasticity:
vertical
0
0
D
“Inelastic demand”
P
QQ1
P1
Q2
P2
Q rises less than 10%
< 10%
10%< 1Price elasticity
of demand =% change in Q
% change in P=
P falls by 10%
Consumers’ price sensitivity:
D curve:
Elasticity:
relatively steep
relatively low
< 1
D
“Unit elastic demand”
P
QQ1
P1
Q2
P2
Q rises by 10%
10%
10%= 1Price elasticity
of demand =% change in Q
% change in P=
P falls by 10%
Consumers’ price sensitivity:
Elasticity:
intermediate
1
D curve:intermediate slope
D
“Elastic demand”
P
QQ1
P1
Q2
P2
Q rises more than 10%
> 10%
10%> 1Price elasticity
of demand =% change in Q
% change in P=
P falls by 10%
Consumers’ price sensitivity:
D curve:
Elasticity:
relatively flat
relatively high
> 1
D
“Perfectly elastic demand” (the other extreme)
P
Q
P1
Q1
P changes by 0%
Q changes by any %
any %
0%= infinity
Q2
P2 =Consumers’ price sensitivity:
D curve:
Elasticity:infinity
horizontal
extreme
Price elasticity of demand =
% change in Q
% change in P=
Thank You
