1 msu weekend mba program – april 28, 2012 marginal analysis -chapter 1 demand – chapter 2,, pgs...
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MSU Weekend MBA Program – April 28, 2012
Marginal Analysis -Chapter 1
Demand – Chapter 2, , pgs 35-45
Elasticities – Chapter 3
Profit Maximization - Ch. 8, pgs 264-265, pgs 277-300
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I. Marginal Analysis - Definitions
Marginal Benefit – the change in total benefits arising from a change in the managerial control variable, Q (OR the change in total benefits arising from a given choice).
Marginal Cost – the change in total costs arising from a change in the managerial control variable, Q (OR the change in total costs arising from a given choice).
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Marginal Analysis for Profit Maximizing Firm Note first that firms maximize Economic Profits
not Accounting Profits
Accounting Profits= Total Revenue-Accounting Costs
Economic Profits= Total Revenue-Economic Costs
where Economic Costs include opportunity costs
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Opportunity Cost - Definition
The cost of the explicit and implicit resources that are foregone when a decision is made OR the cost of using resources for a certain purpose in terms of the benefit given up by using them in their best alternative way.
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Marginal Analysis for Profit Maximizing Firm Marginal Benefit of a firm’s decision is the
change in Total Revenue attributable to that decision.
Marginal Cost of a firm’s decision is the change in Economic Costs attributable to that decision.
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Example 1: Coffee Shop
Steve Mason works as a lawyer in Chicago and owns a two-story Brownstone. He currently lives on the second story of his Brownstone and leases the first floor out to a travel agency. Steve makes $60,000 per year as a lawyer, pays $80,000 per year in mortgage payments on the Brownstone and leases the first floor for $100,000 per year.
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Example 1 (cont.): Coffee Shop Steve is deciding whether to quit is job and open
a coffee shop on the first floor of his Brownstone (instead of leasing the space to the travel agency). Steve expects the coffee shop’s labor costs to be $40,000 per year and supplies to cost $50,000 per year. What is the minimum expected revenue the coffee shop must generate in order for Steve to quit his job as a lawyer? What assumptions do you need to make?
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Example 2: NBA Finals Suppose you plan to attend game 7 of the NBA
Finals game at United Center in slightly over a month – Kevin Durant versus Derrick Rose. You have purchased a plane ticket for $600, bought a ticket for $300 and booked a hotel room for $500. You are standing in the parking lot of the United Center right before tip-off and someone offers you $1200 for your ticket. Do you take it? What does it depend on?
United Center – Home of YOUR Chicago Bulls
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Here you are!
Michael Jordan is hereIsiah Thomas is here
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III. Marginal Analysis and the Time Value of Money Often, some of the benefits and costs
associated with a given decision/action occur in the future.
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Time Value of Money
What is the Present Value (PV) of $100 in T years if the interest rate is i?
PV=100/(1+i)T
What is the PV of $100 in T years and $150 in Z years if the interest rate is i?
PV=100/(1+i)T+150/(1+i)Z
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Example 3: Skaneateles Bar Sherwood Inn is a bar on Skaneateles Lake (one of the
Finger Lakes in Upstate New York). The manager of Sherwood is deciding whether to buy a large tent for the 4th of July (when the town has fireworks over the lake). The manager would use the tent each 4th of July for a beer garden and expects the tent to last three years. The manager also expects that he would be able to increase the number of drinks sold each July 4th by 2,000. Suppose the price of a drink is $3, the cost of the ingredients in each drink is $1 and that the manager would have $1,000 more in labor costs if he has the beer garden. If the annual interest rate is 10%, what is the maximum the manager is willing to pay for the tent?
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Example 4: My Mom My mom owns a house in the Chicago suburbs which is
currently worth $200,000. If she sells the house, she would rent another place in the suburbs for $15,000 a year which she has to pay at the beginning of the year. Suppose that the expected appreciation on the house is 5% annually. Let the interest rate be 10% annually and assume my mom is indifferent between living in her current house or renting (except for the cost issue). What is the maximum annual maintenance cost on the house my mom should be willing to pay? If the annual maintenance cost is greater than this amount, my mom would choose to rent. Assume the maintenance cost is paid at the end of the year.
Demand analysis - intuition
Marginal Cost/Marginal Benefit analysis of consumers
If Marginal Benefit > Marginal Cost, buy it
If Marginal Benefit < Marginal Cost, don’t buy it
Marginal Benefit is reflected by what consumer is willing to pay. Marginal Cost is price of item.
Individual’s Demand for Gasoline’s (based on individual’s willingness to pay)
Depends on, Individual’s Income Price of Gasoline Prices of Related Goods (automobiles,
bus ticket, etc.) Individual’s Tastes/Preferences Individual’s expectation of future prices
Market Demand for Gasoline
Obtained by summing all individual demands.
Depends on, All factors that affect individuals’ demands Number of Individuals (population)
Graphing DemandSchedule:
QuantityPrice Demanded
10 09 18 27 36 45 54 63 72 81 90 10
Gasoline Market
0123456789
10
0 1 2 3 4 5 6 7 8 9 10
D
Q=Quantity of Gas
P=Price of Gas = $/Q
Market Demand for Gasoline(sum of individual demand curves)
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Demand for Adam Humphrey’s Visa Service (based on individuals’ willingness to pay)
Depends on, Price of Service Individual’s Income Price Associated with Doing it at Burger King How much does the person really want to go
to China or how big a hassle is it to come back.
Number of Individuals going to Chinese Consulate for visa.
Demand for Adam Humphrey’s Visa Service
Law of Demand
Is the relationship between price and quantity demanded positive or negative?Negative (Price and quantity demand move in opposite directions)
Law of demand More of a good will be demanded, the lower its price.
Change in quantity demanded
results from a change in price, all else equal
shown as a movement along the demand curve
Change in demand
results from a change in a factor other than price
shown as a shift of the entire demand curve
Notation
D=Demand QD=Quantity Demanded
Example of Change in Demand due to income change Income Increases At every price, do people
want to buy more or less? For Gasoline, More! Demand increases Shifts right
Gasoline Market
0
2
4
6
8
10
12
0 1 2 3 4 5 6 7 8 9 10
Quantity of Gas = Q
Pri
ce/G
allo
n of
Gas
= P
D0
D1
Normal Good
A good for which demand increases when income increases
Examples:
Premium Beers and wine
Disneyland
Gasoline
Lego Robotic
Income Increases for an Inferior Good
Inferior goods are goods where demand decreases when income increases.
Examples:
Pabst Blue Ribbon Beer
Certain Products at Wal-Mart
Generic Diapers
Income Increases for an Inferior Good Income Increases At every price, do
people want to buy more or less?
Less! Demand
decreases Shifts left
Q
P
D0D1
Change in demand due to change in the price of a related good Substitutes
Two goods that satisfy similar needs or desires
Examples:
Diet Pepsi and Diet Coke Strawberries and Raspberries
Gasoline and Manual Lawn Mowers
Change in demand due to change in the price
of a related good: Substitutes Price of a
substitute good decreases
Demand Decreases
Shifts Left
D1
Q
P
D0
Change in demand due to change in the price
of a related good: Substitutes
What happens if the price of a substitute increases?
Demand Increases/Shifts Right
Change in demand due to change in the price of a related good:
Complements Two goods that are used jointly in consumption.
Examples:Tires and GasolineTires and AutomobilesBeer and Pizza
Change in demand due to change in the price
of a related good: Complements Price of a
complementary good decreases
Demand Increases
Shifts right
D1
Q
P
D0
Change in demand due to change in the price
of a related good: Complements
What happens if the price of a complement increases?
Demand decreases/Shifts left
Change in demand due to...
Tastes
Consumer Report indicates that Lexus SUV
rolls and is unsafe. Population
Out migration from Michigan Expectation of Future Prices
Fill up gas tank before Memorial Weekend
Change in demand
results from a change in a factor other than price
shown as a shift of the entire demand curve
change in anything other than price
Demand = Willingness to PayGasoline Market
0123456789
10
0 1 2 3 4 5 6 7 8 9 10
D
Q=Quantity of Gas
P=Price of Gas = $/Q
P=
Consumer Surplus(The value consumers get from a good but do not have to pay for.)
Types of Elasticities
1. Own Price Elasticity of Demand
2. Income Elasticity of Demand
3. Cross Price Elasticity of Demand
Own Price Elasticity of Demand Defined How sensitive quantity demanded is to
price More formally:
Where means “change”
X
DX
D PQ
%%
Example What is the own price elasticity of demand
for cigarettes? -0.4 Interpret this number: A 1% increase in the price of cigarettes
will lower the quantity demanded by 0.4 %
Example If the government wanted to decrease smoking
by 10 percent, by how much would the government have to increase the price of tobacco?
4.0
10.P%
= .25 = 25%
PQ D
%%
P%
10.4.0
What determines relative price elasticity? Number of substitutes The more substitutes or the closer the substitutes, the… more elastic Time interval The longer time interval the… more elastic Share of budget The larger share of the budget the … more elastic
Ex. Diet Coke
Ex. Gasoline
Ex. Salt
Own Price Elasticity of Demand Why do we care?
1. Tells us what affect a in P will have on revenue
2. Tells us what affect a in P will have on Q (ex: taxes)
Own Price Elasticity of Demand
What sign does it have? Negative, Why? Law of Demand
X
DX
D PQ
%%
Calculating Own Price Elasticity of DemandAt a single point, small changes in P and Q
0123456789
101112
0 1 2 3 4 5 6
Q
P ($
/Q)
A
B
C
D
E
F
G
slopeQP
D
PPQ
QD
D
PP
D
D
*
D
D
QP
PQ
*
D
D
QPQP
X
DX
D PQ
%%
slopeQP
D
1*
Own Price Elasticity and demand along a linear demand curve
The equation for the demand curve below is P = 12-2Q
The slope of the demand curve is -2
0123456789
101112
0 1 2 3 4 5 6
Q
P (
$/Q
)
AB
CD
EF
G
Calculating Own Price Elasticity of Demand @ B
0123456789
101112
0 1 2 3 4 5 6
Q
P (
$/Q
)
AB
CD
EF
G
Point Q P d
A 0 12
B 1 10
C 2 8
D 3 6
E 4 4
F 5 2
G 6 0
21
110
=-5
-5
slopeQP
D
1
slopeQP
D
1)Bpoint(
-∞
-2
-1
-1/2
-1/5
0
Own Price Elasticity of Demand
d <-1 (further from 0) is Elastic
% change in QD > % change in P d>-1 (closer to 0) is Inelastic
% change in QD < % change in P
PQ D
%%
Calculating Own Price Elasticity of Demand
0123456789
101112
0 1 2 3 4 5 6
Q
P (
$/Q
)
AB
CD
EF
G
Point Q P d
A 0 12
B 1 10 -5
C 2 8 -2
D 3 6 -1
E 4 4 -½
F 5 2 -1/5
G 6 0 0
-slopeQ
PD
1
d<-1: Elastic
d>-1: Inelastic
Extremes Perfectly Inelastic completely unresponsive to changes in
priceP
4
5
Q
5
D Ex. Insulin
Extremes Perfectly Elastic completely responsive to changes in
priceP
4
5
Q
5
D
Ex. Farmer Joe’s Corn
Elasticity and Total Revenue
Total revenue is the amount received by sellers of a good. Computed as:
TR = P X Q
Intuition Check
If an item goes on sale (lower price), what will happen to the total revenue on that item?
Elasticity and Total Revenue
Marginal Revenue is the additional revenue from selling one
more of a good. Computed as:
MR = TR/Q
Own Price Elasticity of Demand
0123456789
101112
0 1 2 3 4 5 6
Q
P ($
/Q)
A
B
C
D
EF
G
Pt Q P d TR
A 0 12 -∞
B 1 10 -5
C 2 8 -2
D 3 6 -1
E 4 4 -1/2
F 5 2 -1/5
G 6 0 0-22-21-20-19-18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2-101
0 1 2 3 4 5 6
Q
Ela
stic
ity
Own Price Elasticity of Demand
0123456789
101112
0 1 2 3 4 5 6
Q
P ($
/Q)
A
B
C
D
EF
G
Pt Q P d TR
A 0 12 -∞
B 1 10 -5
C 2 8 -2
D 3 6 -1
E 4 4 -1/2
F 5 2 -1/5
G 6 0 0
0
10
16
1816
10
0
0123456789
10111213141516171819
0 1 2 3 4 5 6
Q
TR
=T
E
MR
10
6
2-2-6
-10
Income Elasticity of Demand Defined How sensitive quantity demanded is to
income More formally:
MQDX
M
%%
Where means “income”
Interpreting Income Elasticity
Suppose Income elasticity is 2
A 1 percent increase in income leads to a...
2 percent increase in quantity demanded
MQDX
M
%%
Sign of Income Elasticity
Positive Normal Good Negative Inferior Good M
QDX
M
%%
Ex. Spam
Ex. Great Harvest Bread
Cross-price Elasticity of Demand Defined How sensitive quantity demanded of X is
to a change in the price of Y More formally:
Y
DX
XY PQ
%%
Where PY means “price of Y”
Sign of Cross Price Elasticity
Positive substitutes Negative complements Y
DX
XY PQ
%%
Ex. Accord and Taurus , Diet Coke and Diet Pepsi
Ex. Pizza and Beer, gasoline and SUVs, software and hardware
Words of Caution
There are many complicated issues associated with estimating elasticities. To accurately estimate these elasticities, one needs detailed knowledge of the product/industry, sophisticated statistical techniques, reasonable variation in prices/quantities and precise data.
Costs and Profit Maximization assuming:1. Firm must charge every consumer the
same price (i.e., no price discrimination) 2. No Strategic Interaction among Firms
Think Monopoly
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Firm’s CostsQ FC VC TC AFC AVC ATC MC
0 100 0 100 - - - 50
1 100 50 150 100 50 150
30
2 100 80 180 50 40 90
20
3 100 100 200 33.3 33.33 66.7
10
4 100 110 210 25 27.5 52.5
20
5 100 130 230 20 26 46
(150-100)/1=Fixed costs do not vary with output
Variable costs increase by 50 from 0 to 1 unit of output and increases by 30 from 1 to 2 units.
Average Fixed Costs (AFC) = Fixed Costs/Q so at an output of 2, AFC=100/2=50.
Average Variable Costs (AVC) = Variable Costs/Q so at an output of 2, AVC=80/2=40.
Average Total Costs (ATC) = Total Costs/Q so at an output of 2, ATC=180/2=90 or AFC+ATC.
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Costs Q FC VC TC AFC AVC ATC MC
5 100 130 230 20 26 46
30
6 100 160 260 16.7 26.67 43.3
40
7 100 200 300 14.3 28.57 42.9
50
8 100 250 350 12.5 31.25 43.8
60
9 100 310 410 11.1 34.44 45.6
70
10 100 380 480 10 38 48
Q AFC AVC ATC MC 0 - - - 50
1 100.00 50.00 150.00 30
2 50.00 40.00 90.00 20
3 33.33 33.33 66.67 10
4 25.00 27.50 52.50 20
5 20.00 26.00 46.00 30
6 16.67 26.67 43.33 40
7 14.29 28.57 42.86 50
8 12.50 31.25 43.75 60
9 11.11 34.44 45.56 70
10 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
What output maximizes profits if the marginal revenue (MR) for each unit the firm sells is $55? What are these profits?
8 55*8-43.75*8=90
Q AFC AVC ATC MC 0 - - - 50
1 100.00 50.00 150.00 30
2 50.00 40.00 90.00 20
3 33.33 33.33 66.67 10
4 25.00 27.50 52.50 20
5 20.00 26.00 46.00 30
6 16.67 26.67 43.33 40
7 14.29 28.57 42.86 50
8 12.50 31.25 43.75 60
9 11.11 34.44 45.56 70
10 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
What output maximizes profits if the marginal revenue for each unit the firm sells is $35? What are these profits?
6 35*6-43.33*6=-50
Produce an output of 6 in short-run if fixed costs are sunk.
Q AFC AVC ATC MC 0 - - - 50
1 100.00 50.00 150.00 30
2 50.00 40.00 90.00 20
3 33.33 33.33 66.67 10
4 25.00 27.50 52.50 20
5 20.00 26.00 46.00 30
6 16.67 26.67 43.33 40
7 14.29 28.57 42.86 50
8 12.50 31.25 43.75 60
9 11.11 34.44 45.56 70
10 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
What output maximizes profits if the marginal revenue for each unit the firm sells is $25? What are these profits?
5? 25*5-46*5=-105
Better off producing 0 so profits=-FC=-100
Short-Run Profit Maximizing Rule
Produce at an Output where
Marginal Revenue = Marginal Cost
(MR) (MC)
if Total Revenue > Variable Cost
[When the firm cannot price discriminate, this is the same thing as saying as long as
Price > AVC (from P*Q > AVC*Q) ]
Monopoly Characteristics
1. There is a single seller
2. There are no close substitutes for the good
3. There are extremely high barriers to entry
Monopolist Marginal Revenue (with no price discrimination)
P Q TR MR
10 0 0
9 1 9
8 2 16
7 3 21
6 4 24
5 5 25
4 6 24
3 7 21
2 8 16
1 9 9
0 10 0
+7+5+3
+1-1-3-5-7-9
Q
TRMR
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
D
+9
MR
Q
Note that Marginal Revenue for a given unit is plotted at the midpoint of that unit.
Monopoly If the firm’s goal were to
maximize total revenue, where would it produce?
The elastic and inelastic portions of the demand curve are labeled. How do these relate to MR?
P=$5; D=-1; TR=$25
Elastic: MR>0 Inelastic: MR<0 Will a monopolist ever produce
on the inelastic portion of the demand curve? No.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
D
Elastic
Inelastic
Q
MR
Own Price Elasticity of Demand
0123456789
101112
0 1 2 3 4 5 6
Q
P ($
/Q)
A
B
C
D
EF
G
Pt Q P d TR
A 0 12 -∞
B 1 10 -5
C 2 8 -2
D 3 6 -1
E 4 4 -1/2
F 5 2 -1/5
G 6 0 0
0
10
16
1816
10
0
0123456789
10111213141516171819
0 1 2 3 4 5 6
Q
TR
=T
E
MR
10
6
2-2-6
-10
Monopoly Maximizing Profits
If the monopolist maximizes profits, where would it produce?
At an output where MR=MC as long as P>AVC.
This is at an output of Q=4 so a price of P=6.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
Q
MR
Monopoly Maximizing Profits At Q=4 and P=6, what
is Total Revenue?TR=P*Q=6*4=24 At Q=4, what are Total
Costs?TC=ATC*Q=4.5*4=18 At Q=4 and P=6, what
are Profits?Profits=TR-TC=24-18=6OrProfits=P*Q-ATC*Q
=(P-ATC)*Q=(6-4.5)*4=6
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
Q
MR
TR
TC
Profits
Monopoly Maximizing Profits
What is the difference between these costs and the costs on the prior slide? FC are greater on the costs depicted to the right.
If the monopolist maximizes profits, where would it produce?
Q=4 so set P=6. Profits would be:TR-TC=6*4-8*4= -8
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
MR
Profits
Monopolist in Long Run What should this
monopolist do in the Long Run assuming that the monopolist thinks his costs will not change and neither will demand?
Keep producing Q=4 or change plant size depending if there is a plant size that would result in greater profits.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
Q
MR
Profits
Short Run and Long Run ATCs
Q
Monopolist in Long Run
What should this monopolist do in the Long Run assuming that the monopolist thinks his costs will not change and neither will demand?
Exit the industry or change plant size depending if there is a plant size that would result in positive profits given demand curve.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
MR
Profits
Review of Profit Maximization (when setting a single price)
Marginal Revenue from 5th Unit is just the shaded area below. This area is $11.
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MR
When the MR curve is linear, the area under the MR curve can be obtained by just taking the MR at the midpoint of the quantities – in this case at 4.5.
The orange area is the same as the purple area.
Marginal Cost of 5th Unit is just the shaded area below. This area is $9.
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MRThe purple area is the same as the red area
When the MC curve is linear, the area under the MC curve can be obtained by taking the MC at the midpoint of the quantities – in this case at 4.5.
Change in Profits associated with producing 5 Units rather than 4 units.
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MR
Yellow area is change in profits associated with producing 5 units rather than 4 units. This area is $2.
Subtract MC of 5th unit from MR of 5th unit– brown area from purple.
Review of Profit Maximization (when setting a single price)
PROFIT MAXIMIZATION
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MR
11.2
15
Profits are maximized at an output where MR=MC which is Q=5. Price is 15 and ATC is 11.2 at Q=5.
Profits are then 15*5-11.2*5=19