Transcript M < c - Vitali Alexeev

BEA683 Economics for
Managers
Lecture 1 by Vitali Alexeev
CRICOS Provider Code: 00586B
Tasmanian School of Business and Economics
University of Tasmania
Why Study Economics?

Who does your business interact with?

How does it interact with different parties?

When is it desirable to cooperate or compete?
Where us your business in the marketplace?

Market location – determined by interactions and relationships between your
business and other participants in the process of buying and selling products.

Market location – given by the complex web of interactions between market
players and your business (the value net).
The Value Net
(e.g. Qantas)
Constraints and Opportunities

Economics helps to determine the competitive environment and to
understand the constraints and opportunities that face your business.
Opportunities
Constraints
Investing in a new project
Financial
Expansion to a new market
Labor
Merger/Takeover
Supply
Demand
Policy
Constraints

FINANCIAL: access to capital, inflation and rising interest rates. E.g., Inflation could
mean increased raw material and labor costs, which would affect profitability. Similarly,
rising interest rates mean higher interest payments.

LABOR: skilled employees at affordable wages. Larger companies that can offer more job
security and better compensation packages. Companies can manage labor shortages by
becoming learning organizations, which involves investing in skills training and offering
stock options and other incentives to attract and retain talent.

SUPPLY: a network of suppliers, manufacturers, distributors, retailers and logistics
providers that allow businesses to get their products to consumers. (e.g. March 2011
Japanese earthquake). Diversify supply chains to protect against shortages and
unexpected events, such as fire or flood, BUT diversification could mean additional costs
for small-business owners.

DEMAND: Falling demand = lower revenues. Small businesses cannot grow without
sufficient consumer demand while large businesses might have to scale back
manufacturing capacity or close retail outlets. A sudden surge in demand could also be a
problem if a company does not have the production capacity to meet the demand.
Competitors (limit potential profit)

POLICY: Increasing payroll taxes could raise operating costs. Fiscal deficits could lead to
higher interest rates, which would also reduce profitability. Tariffs and quotas, wage and
price controls.
Economic decision-making

Economics profit vs. accounting profit
Accounting profit = Total revenue – Total accounting costs
Economic profit = Accounting profit – Total implicit opportunity cost
Economic profit = Total revenue – Total economic costs
Example: Economic Profit

Consider the start-up company for which we calculated an accounting profit
of $300,000 and

suppose that the entrepreneurial executive who launched the start-up took a
salary reduction of $100,000 per year relative to the job he left.

That $100,000 is an opportunity cost of involving him in running the start-up.

Besides labor, financial capital is a resource. Suppose that the executive, as
sole owner, makes an investment of $1,500,000 to launch the enterprise and
that he might otherwise expect to earn $200,000 per year on that amount in a
similar risk investment.

Total implicit opportunity costs are $100,000 + $200,000 = $300,000 per year
and economic profit is zero: $300,000 - $300,000 = $0.
Examples of economic profit origins for
a firm

competitive advantage;

exceptional managerial efficiency or skill;

difficult to copy technology or innovation (e.g., patents, trademarks, and
copyrights);

exclusive access to less-expensive inputs;

fixed supply of an output, commodity, or resource;

preferential treatment under governmental policy;

large increases in demand where supply is unable to respond fully over time;

exertion of monopoly power (price control) in the market; and

market barriers to entry that limit competition.
Creating value and bargaining

Businesses earn money by receiving payments from their customers that
exceed the payments to their suppliers

Customers will not pay a firm more for a product than the value of the
benefits they derive from that product

Suppliers will not accept payments that do not cover their own costs.

If there is something to be left for the firm (to earn profit) customers’
benefits must exceed suppliers’ costs!
Key role of economic analysis for managers is to identify the source of value and
understand how this value is divided between various market players.
Consumer surplus and Producer surplus
Consumer Surplus: Value minus Expenditure and Willingness-to-pay

Consider the last thing you purchased.

Maybe it was a cup of coffee, a new pair of shoes, or a new car.

Whatever it was, think of how much you actually paid for it.

Now contrast that price with the maximum amount you would have been
willing to pay for it instead of going without it altogether.

If those two numbers are different, we say you received some consumer
surplus from your purchase.

You received a "bargain" because you were willing to pay more than you had
to pay.
Willingness-to-pay

Law of demand says that as price falls, consumers are willing to buy more of the
good.

Alternatively, we could say that the highest price that consumers are willing to
pay for an additional unit declines as they consume more and more of it.

In this way, we can interpret their willingness to pay as a measure of how much
they value each additional unit of the good.

Important: To purchase a unit of some good, consumers must give up something else
they value.

So the price they are willing to pay for an additional unit of a good is a measure of
how much they value that unit, in terms of the other goods they must sacrifice to
consume it.
Example: Consumer surplus
Example: Producer surplus
Consumer and Producer surplus
Individual decision-making

How to frame a decision and then solve it to eliminate undesirable options
and work out what the most desirable option may be

Decision tree: a tool to frame a decision

Rollback: a method to solve it
Example: Software development (Gans
p.15)

Consider further software development.

Two challenges:


Technical issue: ensure a well functioning product on mobile phones

Marketing issue: distributing the product to mobile phone
Is this too risky to engage in $200,000 expenditure necessary to develop the
upgrade?
Develop and
spend $200,000
Take risk on the
development and
consider whether to
market to mobile
customers
C
Do not develop
and spend $0

Profits from the
handheld markets only
Suppose there are two possibilities with equal probability of occurring
(50/50):

the project is a success and the technical issues are fully sorted out

the project is a failure and the mobile product will be of lower value to customers.
Success (50%)
Develop and spend
$200,000
Take risk on
the
development
Failure (50%)
C
Do not develop and
spend $0

Consider whether
to enter to mobile
market
Consider whether to
enter to mobile
market
Profits from
the handheld
markets only
This, however, still incomplete decision tree. The decision of whether to
enter the mobile market is considered following the resolution of uncertainty
regarding whether the project is successful or not.
Enter
Consider whether
to enter to mobile
market
Success (50%)
Develop and spend
$200,000
Don’t Enter
Profits from handheld
markets only
Take risk on the
development
Failure (50%)
C
Do not develop and
spend $0
Profits from the
handheld
markets only

Profits in handheld and
mobile markets
Consider whether to
enter to mobile
market
Enter
Don’t Enter
Profits in handheld and
mobile markets
Profits from handheld
markets only
This decision tree presents qualitative information only. Next slide presents
the same decision tree where the quantitative information is utilized.
Enter
Profits in handheld (h)
and mobile markets (M)
Consider whether to
enter to mobile
market
Don’t Enter
Success (50%)
Develop and spend
$200,000
Profits from handheld
markets only (h)
Take risk on the
development
Failure (50%)
C
Do not develop and
spend $0

Consider whether to
enter to mobile
market
Profits from the
handheld markets
only (h)
Enter
Don’t Enter
Profits in handheld (h) and
mobile markets (m)
Profits from handheld
markets only (h)
Note that M are the profits from the mobile markets is the project is a
success and m are the profits from the mobile markets is the project is a
failure.
h+M-c-200,000
Enter
Consider
whether to enter
to mobile market
Success (50%)
Don’t Enter
h-200,000
Develop
Take risk on the
development
h+m-c-200,000
Failure (50%)
C
Consider whether
to enter to mobile
market
Do not develop
h

Enter
Don’t Enter
Note that M are the profits from the mobile markets is the project is a
success and m are the profits from the mobile markets is the project is a
failure. c are the costs of entry.
h-200,000
Solving the tree

Your first decision is whether to develop the upgrade or not.

However, in order to calculate the benefits from this you need to anticipate
any subsequent decision you might make and the uncertainty that you face.

If the project is a success, you would only choose to Enter if:
h + M – c - 200,000 > h – 200,000
h + M – c - 200,000 > h – 200,000
M>c

The entry decision does not depend on handheld market profits (h) or
development costs (200,000).

It will be worthwhile to enter the mobile market only if the profits (M)
exceed the cost of entry (c).
Solving the tree

Similarly, if the project is not a success, you would only choose to Enter if:
h + m – c - 200,000 > h – 200,000
h + m – c - 200,000 > h – 200,000
m>c

The entry decision does not depend on handheld market profits (h) or
development costs (200,000).

It will be worthwhile to enter the mobile market only if the profits (m)
exceed the cost of entry (c).

i.
ii.
There are three cases to consider:
M < c, and therefore, m < c

only sell in the handheld market

whether the project is successful or not is irrelevant
m > c and therefore, M > c

iii.
always choose the mobile market
M>c>m

only enter the mobile market is the project is successful.
Payoffs under different scenarios
Case
If project developed
If project not
developed
i. M < c and m < c
h-200,000
h
ii. m > c and M > c
0.5(h+M-c-200,000)+0.5(h+m-c-200,000)=
h
h+0.5(M+m)-c-200,000
iii. M > c > m
0.5(h+M-c-200,000)+0.5(h-200,000)=
h+0.5(M-c) -200,000
(note: typo in Fig 2.7 on p.21 in Gans)
h
Solving the tree

By using roll-back, the decision tree can be reduced to some simple
calculations

If M < c then developing the software is not worthwhile as entry into the
mobile market is not profitable

If m > c, then it is worthwhile to develop if h+0.5(M+m)-c-200,000 > h or
(M+m)/2-c > 200,000

However, if entry into the mobile market is only profitable for a successful
development (M > c > m), then the development decision is based solely on
the expectation of that success.
E.g., h+0.5(M-c) -200,000 > h or
(M-c)/2 > 200,000
Common decision-making pitfalls

Sunk costs



Costs that already been incurred and cannot be recovered. When making decisions,
managers should ignore these costs; otherwise, they risk making poor decisions.
Marginal vs average costs

When considering increasing or decreasing production levels, firms should base
their decisions on marginal costs (MC) rather than average costs (AC).

MC accurately reflects the cost of producing an additional unit of output or the
savings from producing one unit less.
Economic vs accounting profits

Consider not only the explicit costs, but also the opportunity cost, implicit cost
such as revenues that the inputs could have generated through some other use.
Cooperative decision-making

Many decisions are not individual (as in the example before) but joint or
cooperative.

The outcomes on the tips of the branches of decision trees involve the sume
of the values of all of the individuals involved when they either do or do not
cooperate respectively.

In business, cooperative decision is whether to trade or exchange goods and
services.

Two parties decide whether they will be jointly better off by trading as
opposed to not trading. Trade will only occur if there is value created from it.
Creating value through exchange
Example

Vases Abroad Inc. are importers of rare vases from China.

Each vase has a unique value to a potential customer (𝑣𝐵 - value to the buyer)
and also a distinct acquisition cost for Vases Abroad.

Vases Abroad has acquired a Ming Dynasty era vase.

A particular customer, Ming21 (a dealer), has expressed interest in purchasing
it.

If Vases Abroad don’t sell the vase to Ming21, they believe that the expected
price they would receive from other customers would be about $50,000,
although it would take some time to sell the vase.

The storage, security and insurance costs will amount to $2,000.

Is it worthwile to sell the vase to Ming21?
Trade vase to
Ming21
𝑣𝐵
Vases Abroad
and Ming21
Don’t trade vase
to Ming21
$48,000
Example…continued

It will be jointly desirable for Vases Abroad to trade the vase to Ming21 if 𝑣𝐵 is at
least $48,000.

The difference in joint payoffs (𝑣𝐵 -$48,000) is the value created by this exchange or
the gains from trade.

In general, if a good is bought by a buyer who places a value, 𝑣𝐵 , on the good, and
sold by a seller who would otherwise earn 𝑜𝑆 (𝑜𝑆 = $48,000), then there is value
created by an exchange only if 𝑣𝐵 > 𝑜𝑆 .

Sometimes it will be the case that the exchange may free the seller up to engage in
other activities allowing them to earn, say, 𝑣𝑆 .

It may also be the case, if no trade takes place, the buyer would use his funds to
pursue other opportunities and netting earnings of 𝑜𝐵 .

In this general case, there is value created from the exchange only if:
𝑣𝐵 + 𝑣𝑆
𝑗𝑜𝑖𝑛𝑡 𝑝𝑎𝑦𝑜𝑓𝑓
≥ 𝑜𝑆 + 𝑜𝐵
What about price?
A trade will only take place at a price that makes both the buyer and the seller
individually better of as a result of the exchange.
(a) Ming21
(b) Vases Abroad Inc
𝑣𝐵 − 𝑝
Buy vase from
Vases Abroad
𝑝
Vases
Abroad
Ming21
Don’t buy
$0
Sell vase to
Ming21
Don’t sell to
Ming21
$48,000

A trade will only take place at a price that makes both the buyer and the
seller individually better of as a result of the exchange. That is:
𝑣𝐵 − 𝑝 ≥ 𝑜𝐵 and 𝑝 − 𝑣𝑆 ≥ 𝑜𝑆

Putting the two together (note: typo in Guns on p.31):
𝑣𝐵 − 𝑜𝐵 ≥ 𝑝 ≥ 𝑜𝑆 −𝑣𝑆

That is a range of prices may exist if
𝑣𝐵 − 𝑜𝐵 > 𝑜𝑆 − 𝑣𝑆 or 𝑣𝐵 + 𝑣𝑆 > 𝑜𝐵 + 𝑜𝑆

A customer’s willingness-to-pay is the maximum price they would pay and still
choose to purchase a product. E.g. 𝑝 = 𝑣𝐵 − 𝑜𝐵

A supplier’s willingness-to-sell is the minimum price they would accept and
still choose to supply a product. E.g. 𝑝 = 𝑜𝑆 − 𝑣𝑆
Identifying player roles


Customer: any player who pays money to the business

Often, easy to identify; but, e.g. Red Cross that is in the business of helping those
in need.

Can have more than one class of customers
Supplier: any player who receives money from the business

Employees, equipment manufacturers, energy/utilities providers;

E.g. savings and chequeing bank account depositors.
Willingness-to-pay and willingness-to-sell

Willingness-to-pay: a concept that not only depends on the direct benefits
from a product but depends on the alternatives that face the customer (e.g.
hotel mini-bar).

Willingness-to-sell: by supplying resources or inputs to a business, the
suppliers are unable to supply these resources elsewhere. This lost
opportunity for alternative earnings is the opportunity cost incurred by
suppliers.
Value Creation with Many Agents
Many customers and sellers

Demand: For each unit price of a product, the quantity demanded for a
product is the quantity of output for which a customer’s willingness-to-pay for
a unit of output exceeds price.

Supply: For each unit price of a product, the quantity supplied of a product is
the quantity of output for which suppliers’ willingness-to-sell for a unit of
output exceeds price.
Co-Operating with Complementors

An agent is your complementor if customers value your product more when
they have the other agent’s product than when they have your product alone.

Interdependent industries often co-operate to achieve greater profitability.

The existence of and demand for complementary products can improve
industry profitability. After all, complementary products stimulate demand for
an industry's products.

E.g., a customer is willing to pay more for fish and chips when they are both
available than fish and chips separately.
Viewing complementarity on the supply-side

A player is your complementor if it is more attractive for a supplier to
provide resources to you when it is also supplying the other player, than when
it is supplying you alone.

If a particular supplier has a greater willingness-to-sell to you and another
customer together than to each separately, then you and the other customer
are complementors in supply.

E.g., some use a broadband during the day while others use it at night. If both
types of customers are available, an Internet provider can provide the service
to each at a lower price than it could if only one type were available.
Demand, Supply & Markets
A market is a group of buyers and sellers of a
particular good or service.
Buyers determine the level of demand in the
market, and sellers determine the level of
supply.
Types of markets:
Perfect
Competition
Many buyers
Many sellers
Oligopoly
Monopolistic
Competition
Many buyers
Few sellers
Many buyers
Few sellers
Increase in sellers’ bargaining power
Monopoly
Many buyers
One seller
Competitive Market Assumptions
An individual is a price-taker if they are unable to influence the
traded price.
In a competitive market, this is a reasonable assumption:
individuals observe the price then decide whether to trade or not.
We will be focusing on a model of competitive markets,
which is supported by the following assumptions:
• Many buyers
• Many sellers
• Homogeneous good
• Full information
• Price-taking
behaviour
• No externalities
Informational requirements:
– All prices that traded.
– The existence and location of all the
sellers.
– The exact characteristics of
good/service.
– All buyer’s valuations
42
– All seller’s valuations.
Demand and Supply
Discrete
Continuous
Shifts in Demand vs shifts along the
demand curve
Shifts in Supply vs shifts along the
supply curve
Demand Schedule, Demand Curve
Demand Curve
P($ / unit )
Demand Schedule
10
7
5
4
2
1
0
1
2
3
4
5
6
Price
($/unit)
Qty
Demanded
1
6
2
5
4
4
5
3
7
2
10
1
Q
Characteristics of Demand
Demand curve shifts right when:
P($ / unit )
(i)
There is an increase in the price of
a substitute good;
(ii) A decrease in the price of a
complement good;
(iii) An increase in the individual’s
income?
(iv) A favourable change in tastes.
10
7
Note: a change in the price of a
good results in a movement
along its demand curve.
5
4
2
1
D
0
1
2
3
4
5
6
Q
D'
47
Market Demand
The market supply curve is the horizontal
sum of the supply curve of each firm in
the industry.
P($ / unit )
10
D1
D2
Firm 2
Demand
7
5
4
Market
Demand Curve
Firm 1
Demand
DTotal
2
1
0
1
2
3
4
5
6
7
Q
48
Price Sensitivity of Demand
Consider two measures of the price sensitivity of demand:
Q
(i ) s1 
P
P($ / unit )
D
21
C
19
7
Q / Q
(ii ) s2 
P / P
Using the first measure, the quantity
demanded response from A to B is the same
as from C to D…?
Note that measure (i) depends on
the units that quantity is
measured in –whereas measure
(ii) is unit-free.
B
5
A
D
0
1 2
9 10
Q
49
Elasticity of Demand
Note (-)
sign
Definition: the price of price elasticity of
QA / QA
demand for good A measures the % change in the A  
PA / PA
quantity demanded for a 1 % change in its price:
Definition: the cross price of
price elasticity of demand for
good A with respect to the
price of good B measures the %
change in the quantity
demanded for good A of a 1 %
change in the price of good B:
Definition: the income
elasticity of demand for good A
is the % change in quantity
demand of good A when income
(Y) changes by 1 %:
 A, B
Q A / Q A

PB / PB
 A, B
 0  A & B are substitutes

  0  A & B are complements
 A,Y
 A,Y
Q A / Q A

Y / Y
 0  A is a normal good

  0  A is an inferior good
50
Demand Elasticity
Linear demand for good X
P($ / unit )
Polar cases
P($ / unit )
Elastic
X  1
Unit elastic
X  1
Inelastic
M
X  1
X  0
X  
D
0
Q
51
Q
52
Source: Allen, Bruce T, Managerial Economics, 1994
53
Source: Allen, Bruce T, Managerial Economics, 1994
Supply
The supply side of the market is controlled by the
producers of the good or service.
OUTPUTS
INPUTS
• Labour (L)
Production
• Capital (K)
Q  f ( L, K )
• Final consumption goods
• Intermediate goods
• Services
Eg.
Inputs: plant, press,
robots, assembly workers,
engineers, designers,
managers, steel, rubber,
glass, components…
Combine with
technology
Output:
passenger
54
vehicle
Production Function
Definition: the production function summarises
the relationship between:


the quantity of inputs and

the maximum quantity of outputs

given a particular technology.
The production function includes only
efficient production processes

ie. workers are not shirking, capital is not
broken…
55
Production Function
Q  f ( K , L)  TP
# of units of output:
K ≡ # of units of capital
L ≡ # of units of labour
f (.) is a rule representing
the current technology.
Examples:
Capital (K)
Q  f ( K , L)
 2 KL
Labour (L)
Q
1
2
3
4
5
1
2
4
6
8
10
2
4
8
12
16
20
3
6
12
18
24
30
4
8
16
24
32
40
5
10
20
30
40
50
56
Production Function: Q = 2KL
50
45
40
35
45-50
30
40-45
25
35-40
20
30-35
15
25-30
10
20-25
5
15-20
0
10-15
5
5
4
4
3
3
2
5-10
0-5
2
1
57
Production Function: Q=K1/2L1/2
1600
1400
1400-1600
1200
1200-1400
1000
1000-1200
800
800-1000
600-800
600
400-600
200-400
400
0-200
200
0
10
9
8
7
6
5
4
3
2
1
2
3
4
5
6
7
8
9 10
58
Production with One Input
Definition: the marginal product of labour is the
amount of additional output produced if labour is
increased by one unit:
L
L
MPL 

≡ slope of production function
Q f ( L)
Definition: the average product of labour is the
average output produced per unit of labour:
Q
≡ slope of ray to production
APL 
L function
59
Law of Diminishing Marginal Returns

At small levels of production, if a firm increases its input
then it can yield large gains in output, eg. from division of
production tasks.

In terms of labour input, this is referred to as increasing
marginal product of labour.

If a firm keeps increasing an input, holding all other
inputs and technology constant, the return on the inputs
in terms of increases in output will eventually become
smaller.

In terms of labour input this is referred to as the
diminishing (or decreasing) marginal product (or return) of
labour.
60
Q
Q4
Q3
Total, Marginal and
Average Product
f (L)
Q2
How are TP, AP and MP related?
Q1
MPL
APL
L1
L2
L3
L4 L5
MPL
L
When MPL  APL  APL 
When MPL  APL  APL 
APL
L1
L2
L3
L4
When MPL  APL  APL
L
is at its max .
L5
61
Returns to Scale
TP
TP  f (L)
IRS
CRS
DRS
L
An increase in L
increases TP more
than proportionally.
A one unit increase
in L increases TP
proportionally.
An increase in L
increases TP less than
proportionally.
62
ie. MP is increasing. ie. MP is constant. ie. MP is decreasing.
Cost of Production
Definition: the total cost of production, TC, of Q units of output
is equal to the sum of the expenditures on each input:
TC (Q)  wL(Q)  rL(Q)  VC (Q)  FC
Definition: the average cost of production, AC, of Q units of
output is equal to:
AC (Q)  TC (Q) / Q
Definition: the marginal cost of production, MC, is the amount that
total increases when output is increased by one unit:
MC (Q)  TC (Q) / Q
63
Relationship Between Production &
Cost
Recall:
w
w
w L
TC VC



MC 

Q / L MPL
Q
Q
Q
Recall also that we analysed an “S” shaped production function, where for
small levels of labour the production had increasing marginal returns from
specialisation and division of tasks, then for higher levels of labour
constant marginal returns, then for even higher levels of labour the
amount of fixed capital became diluted enough that the diminishing
marginal returns set in.
The relationship between MC, w and MPL above can be used to
rationalise the shape of the cost curves...
64
Relationship Between Production & Cost
TC  FC  VC
TC
VC
FC
IMR
CMR
DMR
Q
A one unit increase in Q
requires smaller
increases in L, so MC
increases at a smaller
rate.
A one unit increase in Q A one unit increase in Q
requires a proportional requires larger increases
increase in L, so MC
in L, so MC increases at
increases proportionally. a greater rate. 65
Q
TC
Total, Marginal and
Average Cost
When MC  AC  AC 
When MC  AC  AC 
FC
Q1
MC
AC
Q2
Q3
Q4
When MC  AC  AC
is at its max .
Q
AC
MC
Q1
Q2
Q3
Q4
Q
66
Willingness-to-Sell
Recall: the Willingness to Sell (WTS) a unit of good X is
the minimum dollar sum of revenue that a firm is willing
to accept to produce another unit of good X instead of
some other good.
Hence, WTS is the firm’s opportunity cost of producing a
unit of its good, measure in dollars, and it equal to the
marginal cost of production.
 WTS is the MC curve, which in turn is the firm’s supply
curve!
67
Supply Schedule, Supply Curve
Supply Curve
P($ / unit )
Supply Schedule
S
10
7
6
5
4
Price
($/unit)
Qty
Demanded
2
1
4
2
5
3
6
4
7
5
10
6
2
0
1
2
3
4
5
6
68
Q
Characteristics of Supply
Supply curve shifts right when:
P($ / unit )
S
10
7
5
4
(i)
There is an
improvement in
technology;
(ii) A change in the price of
an input;
(iii) A change in the
S'
production plans of the
industry.
Note: a change in the
price of a good results in a
movement along the
supply curve.
2
1
0
1
2
3
4
5
6
69
Q
Market Supply
The market supply curve is the horizontal sum of the
supply curve of each firm in the industry.
Firm 1 Supply
P($ / unit )
10
Firm 2 Supply
S1
STotal
S2
7
5
4
Market Supply
Curve
2
1
70
0
1
2
3
4
5
6 7 Q
Market Equilibrium
Putting together the supply and demand sides of the market yields:
P($ / unit )
SURPLUS
S
10
If the price is high:
Quantity  Quantity
supplied
demand
 Surplus: not all units are traded
If the price is low:
Quantity  Quantity
supplied
demand
7
5
4
 Shortage: too few units are traded
Market
Equilibrium:
2
1
D
SHORTAGE
0
1
2
3
4
5
6
D(Q )  S (Q )
Where on the last unit traded:
WTP  WTS  p
71
Q
Comparative Statics
Consider the market for donuts. Suppose the price of coffee decreases.
P($ / unit )
S
10
Since donuts and coffee are
complements, the demand
curve for donuts shifts right
for each level of the price.
If the price stays at the same
level, then the new quantity
demanded at that price is
greater than the quantity
supplied.
7
5
4
 Shortage: too few units of
donuts are traded.
D'
SHORTAGE
2
1
The price of donuts will
increase until:
D
0
1
2
3
4
5
6
D(Q )  S (Q )
72
Q
Strategic decision-making
Type of games
74
Example 1: A Rollback Solution




Sequential moves are strategies where there is a strict
order of play.
Perfect information implies that players know
everything that has happened prior to making a
decision.
Complex sequential move games are most easily
represented in extensive form, using a game tree.
Chess is a sequential-move game with perfect
information.
Example 1: A Rollback Solution
Backward induction or rollback solves sequential move
games with perfect information by rolling back optimal
strategies from the end of the game to the beginning.
Example 1: A Rollback Solution
Century Mark Game

Played by pairs of players taking turns.

At each turn, each player chooses a number between 1 and 10
inclusive.

This choice is added to sum of all previous choices (the initial
sum is 0).

The first player to take the cumulative sum to 100 or more
wins.
How should you play the game as first player? Start at the end.
What number gets you to 100 next turn?
Example 1: A Rollback Solution
Rollback Solution
 If you bring the cumulative sum to 89, you can take the
cumulative sum to 100 and win no matter what your opponent
does. (Whatever your opponent does you can make the sum of
your two moves equal 11.)
 Hence, if you bring the cumulative sum to 78, you can bring the
cumulative sum to 89 on your next turn (and so eventually win)
no matter what your opponent does.
 And so on for sums 67, 56, 45, 34, 23, 12.
 Hence, if you play 1 first, you can bring the cumulative sum to
12 on your next turn (and so eventually win) no matter what
your opponent does.

That is a strategy --- a complete plan of actions no matter what
your opponent does.
Example 2: A Game Tree
Game trees or extensive forms consist of nodes and branches.
Nodes are connected to one another by the branches, and come in
two types.
Some nodes are decision nodes, where a player chooses an action.
In some games, Nature is a “player”; Nature can decide whether it
rains or snows. This is uncertainty.
The other nodes are terminal nodes, where players receive the
outcomes of the actions taken by themselves and all other players.
Example 2: A Game Tree
 Emily, Nina, and Talia all live on the same street. Each has been
asked to contribute to a flower garden.
 The quality of the garden increases with the number of
contributions, but each lady also prefers to not contribute.
 Specifically, suppose each lady gains 2 dollars worth of
happiness from each of the first two contributions to the garden
(including her own contribution, if any) and 0.50 dollars worth
from a third contribution, but then looses 1 dollar if she herself
contributes.
Define the game tree for this Street Garden Game, then find the
rollback solution. Should Emily contribute?
Example 2: A Game Tree
Street Garden Game
Emily
Contribute
Don't
Nina
Nina
Contribute
Don't
Contribute
Don't
Talia
Talia
Talia
Talia
Cont.
Don't
Cont.
Don't
Cont.
Don't
Cont.
Don't
3.5,3.5,3.5
3,3,4
3,4,3
1,2,2
4,3,3
2,1,2
2,2,1
0,0,0
Example 2: A Game Tree
Rolling from the end: Talia’s Strategy. (Non-optimal
strategies are blacked out.)
Emily
Contribute
Don't
Nina
Nina
Contribute
Don't
Contribute
Don't
Talia
Talia
Talia
Talia
Cont.
Don't
Cont.
Don't
Cont.
Don't
Cont.
Don't
3.5,3.5,3.5
3,3,4
3,4,3
1,2,2
4,3,3
2,1,2
2,2,1
0,0,0
Example 2: A Game Tree
Rolling back one from the end: Nina’s Strategy
Emily
Contribute
Don't
Nina
Nina
Contribute
Don't
Contribute
Don't
Talia
Talia
Talia
Talia
Cont.
Don't
Cont.
Don't
Cont.
Don't
Cont.
Don't
3.5,3.5,3.5
3,3,4
3,4,3
1,2,2
4,3,3
2,1,2
2,2,1
0,0,0
Example 2: A Game Tree
Rolling back to the beginning: Emily’s Strategy, which
completes the rollback solution.
Emily
Contribute
Don't
Nina
Nina
Contribute
Don't
Contribute
Don't
Talia
Talia
Talia
Talia
Cont.
Don't
Cont.
Don't
Cont.
Don't
Cont.
Don't
3.5,3.5,3.5
3,3,4
3,4,3
1,2,2
4,3,3
2,1,2
2,2,1
0,0,0
Example 3: Off the Equilibrium Path
Beliefs about strategy off the equilibrium path (strategies
that are never acted on) are important to keep players on
the equilibrium path. Just as your belief that shooting a
gun at your own head will kill you makes you decide to
never shoot a gun at your own head.
Example 3: Off the Equilibrium Path
Street Garden Game:
alternative payoffs
Emily
Contribute
Don't
Nina
Nina
Contribute
Don't
Contribute
Don't
Talia
Talia
Talia
Talia
Cont.
Don't
Cont.
Don't
Cont.
Don't
Cont.
Don't
5,5,5
3,3,6
3,4,3
1,2,2
4,3,3
2,1,2
2,2,1
2,2,2
Example 3: Off the Equilibrium Path
Street Garden Game:
Equilibrium Path
Emily
Contribute
Don't
Nina
Nina
Contribute
Don't
Contribute
Don't
Talia
Talia
Talia
Talia
Cont.
Don't
Cont.
Don't
Cont.
Don't
Cont.
Don't
5,5,5
3,3,6
3,4,3
1,2,2
4,3,3
2,1,2
2,2,1
2,2,2
Example 3: Off the Equilibrium Path
Emily believes that, if she contributed, then Nina would not contribute but
Talia would contribute. But if, instead, Emily believed that, if she
contributed, then Nina and Talia would both contribute, then Emily believes
contributing gives her payoff 5, which is more than her payoff on the
equilibrium path.
Emily
Contribute
Don't
Nina
Nina
Contribute
Don't
Contribute
Don't
Talia
Talia
Talia
Talia
Cont.
5,5,5
Don't
3,3,6
Cont.
3,4,3
Don't
1,2,2
Cont.
4,3,3
Don't
Cont.
Don't
2,1,2
BA 592
Lesson I.3
Sequential
Move Theory
2,2,2
2,2,1
Example 4: Multiple Equilibria
Rollback equilibria are unique unless a player gets equal
payoffs from two or more different actions. One method
to restore a unique equilibrium (to be used as a
prescription or prediction) is to question whether a game
with equal payoffs is somehow exceptional or avoidable.
Example 4: Multiple Equilibria
Employees know there is a positive gain to their continued
employment, and that gain is split with their employer
according to the employees wages. Suppose Employee A
generates 100 dollars of gain by remaining employed with
Employer B. Employee A is considering increasing his
wage demands to one of three levels. Those three levels
give him either 100%, or 90%, or 50% of the 100 dollars of
gain. Which wage should the employee demand?
Define the game tree for this Bargaining Game, then find
all the rollback equilibria.
Example 4: Multiple Equilibria
Bargaining Game:
Game Tree
Proposer
I take 100%
I take 90%
I take 50%
Responder
Responder
Responder
Accept
Reject
Accept
Reject
Accept
Reject
100,0
0,0
90,10
0,0
50,50
0,0
Example 4: Multiple Equilibria
Bargaining Game:
Partial Rollback Solution
Proposer
I take 100%
I take 90%
I take 50%
Responder
Responder
Responder
Accept
Reject
Accept
Reject
Accept
Reject
100,0
0,0
90,10
0,0
50,50
0,0
Example 4: Multiple Equilibria
Rollback analysis was incomplete in that game because
the responder got equal payoffs from two different
actions. But that is only because the Proposer demanded
100%. What if the Proposer demands 99.99%? Now there
is a unique rollback solution with payoffs almost as high as
if a demand of 100% were accepted.
Example 4: Multiple Equilibria
Bargaining Game:
Complete Rollback Solution
Proposer
I take 99.99%
I take 90%
I take 50%
Responder
Responder
Responder
Accept
Reject
Accept
Reject
Accept
Reject
99.99,0.01
0,0
90,10
0,0
50,50
0,0
Example 5: Jealous Humans
Humans in some sequential move games do not follow the
rollback solution because that solution may be felt to be
too unfair.
Economic policymakers thus favor public policies whose
rollback solutions seem fair enough for humans to accept.
And businesspeople thus adapt strategies depending on
whether they are playing against jealous humans (perhaps
some of their customers) or rational players (other
businesspeople).
Example 5: Jealous Humans
Shoppers know there is a positive gain to making
purchases, and that gain is split with sellers according to
the purchase price. Shopper A generates 100 dollars of
gain by buying from Seller B. Buyer A is considering three
alternative price offers. Those three offers give him
either 99%, or 90%, or 50% of the 100 dollars of gain.
Which price should Buyer A offer?
Define the game tree for this Bargaining Game, then find
the rollback solution.
.
Example 5: Jealous Humans
Bargaining Game:
Game Tree
Proposer
I take 99%
I take 90%
I take 50%
Responder
Responder
Responder
Accept
Reject
Accept
Reject
Accept
Reject
99,1
0,0
90,10
0,0
50,50
0,0
Example 5: Jealous Humans
Bargaining Game:
Rollback Solution
Proposer
I take 99%
I take 90%
I take 50%
Responder
Responder
Responder
Accept
Reject
Accept
Reject
Accept
Reject
99,1
0,0
90,10
0,0
50,50
0,0
Example 5: Jealous Humans
Which price should the shopper offer? In the rollback
solution, the shopper should offer the price that gives him
99% of the gain from trade. But humans like the seller
might not follow the rollback solution because that
solution is too unfair. Rather, the shopper may have to
offer a price that gives him only 90% or 50% of the gain
from trade.
Example 6: Simple Humans
Humans in some sequential move games do not follow the rollback
solution because that solution is too computationally complex.
Chess is a sequential move game with perfect information, so it has a
game graph, with an estimated 10120 nodes describing all possible board
positions.
There is a rollback solution, but that solution is so computationally
complex no human knows all of it. It was, therefore, inevitable that
computers eventually became better players than humans.
In May 1997, a chess playing machine “Deeper Blue” beat reigning
champion Garry Kasparov, by 3½ to 2½ in a six game match. Recent
progress in computer play is software than can run on common personal
Example 6: Simple Humans
Humans in other sequential move games do not follow the rollback
solution because that solution is too conceptually complex.
Economic policymakers thus favor public policies whose rollback
solutions are simple enough for humans to compute.
And businesspeople thus adapt strategies depending on whether they
are playing against simple humans (perhaps some of their customers)
or playing against rational players (other businesspeople).
Example 6: Simple Humans
Buyers and Sellers trading over the internet risk sending money or
goods and not getting what was agreed upon. One solution that
minimizes your exposure to fraud is to trade a little at a time.
Example 6: Simple Humans
Suppose Albert values 6 disposable DVDs at $3 each, suppose it costs Blockbuster $1
to provide each DVD, and suppose Blockbuster sells DVDs for $2 each. Should
Blockbuster send the first DVD to Albert?
• If the first DVD is sent, Albert (A) faces a decision: steal the DVD and terminate
the relationship; or, send $2 for the first DVD.
• If the first $2 is sent, Blockbuster (B) faces a decision: take the $2 and terminate
the relationship; or, send the second DVD to A.
• If the second DVD is sent, A faces a decision: steal the DVD and terminate the
relationship; or, send $2 for the second DVD.
• If the second $2 is sent, B faces a decision: take the $2 and terminate the
relationship; or, send the third DVD to A.
• And so on.
• If the sixth DVD is sent, A faces a decision: steal the DVD and terminate the
relationship; or, send $2 for the sixth DVD.
Define the game tree for this Centipede Game (the tree looks like a centipede),
then find the rollback solution.
Example 6: Simple Humans
A
Centipede Game:
Game Tree
Steal 1
Pay 1
3,-1
B
Take 2
Send 2
1,1
A
Steal 2
Pay 2
4,0
B
Take 3
Send 3
2,2
A
Steal 3
Pay 3
5,1
B
Take 4
Send 4
3,3
A
Steal 4
Pay 4
6,2
B
Take 5
Send 5
4,4
A
Steal 5
Pay 5
7,3
B
Take 6
Send 6
5,5
A
Steal 6, payoff 8,4
Pay 6, payoff 6,6
Example 6: Simple Humans
Centipede Game:
A’s sixth choice
A
Steal 1
Pay 1
3,-1
B
Take 2
Send 2
1,1
A
Steal 2
Pay 2
4,0
B
Take 3
Send 3
2,2
A
Steal 3
Pay 3
5,1
B
Take 4
Send 4
3,3
A
Steal 4
Pay 4
6,2
B
Take 5
Send 5
4,4
A
Steal 5
Pay 5
7,3
B
Take 6
Send 6
5,5
A
Steal 6, payoff 8,4
Pay 6, payoff 6,6
Example 6: Simple Humans
Centipede Game:
B’s sixth choice
A
Steal 1
Pay 1
3,-1
B
Take 2
Send 2
1,1
A
Steal 2
Pay 2
4,0
B
Take 3
Send 3
2,2
A
Steal 3
Pay 3
5,1
B
Take 4
Send 4
3,3
A
Steal 4
Pay 4
6,2
B
Take 5
Send 5
4,4
A
Steal 5
Pay 5
7,3
B
Take 6
Send 6
5,5
A
Steal 6, payoff 8,4
Pay 6, payoff 6,6
Example 6: Simple Humans
Centipede Game:
A’s fifth choice
A
Steal 1
Pay 1
3,-1
B
Take 2
Send 2
1,1
A
Steal 2
Pay 2
4,0
B
Take 3
Send 3
2,2
A
Steal 3
Pay 3
5,1
B
Take 4
Send 4
3,3
A
Steal 4
Pay 4
6,2
B
Take 5
Send 5
4,4
A
Steal 5
Pay 5
7,3
B
Take 6
Send 6
5,5
A
Steal 6, payoff 8,4
Pay 6, payoff 6,6
Example 6: Simple Humans
Centipede Game:
B’s fifth choice
A
Steal 1
Pay 1
3,-1
B
Take 2
Send 2
1,1
A
Steal 2
Pay 2
4,0
B
Take 3
Send 3
2,2
A
Steal 3
Pay 3
5,1
B
Take 4
Send 4
3,3
A
Steal 4
Pay 4
6,2
B
Take 5
Send 5
4,4
A
Steal 5
Pay 5
7,3
B
Take 6
Send 6
5,5
A
Steal 6, payoff 8,4
Pay 6, payoff 6,6
Example 6: Simple Humans
And so on, until …
Example 6: Simple Humans
Centipede Game:
B’s first choice
A
Steal 1
Pay 1
3,-1
B
Take 2
Send 2
1,1
A
Steal 2
Pay 2
4,0
B
Take 3
Send 3
2,2
A
Steal 3
Pay 3
5,1
B
Take 4
Send 4
3,3
A
Steal 4
Pay 4
6,2
B
Take 5
Send 5
4,4
A
Steal 5
Pay 5
7,3
B
Take 6
Send 6
5,5
A
Steal 6, payoff 8,4
Pay 6, payoff 6,6
Example 6: Simple Humans
Centipede Game:
A’s first choice
A
Steal 1
Pay 1
3,-1
B
Take 2
Send 2
1,1
A
Steal 2
Pay 2
4,0
B
Take 3
Send 3
2,2
A
Steal 3
Pay 3
5,1
B
Take 4
Send 4
3,3
A
Steal 4
Pay 4
6,2
B
Take 5
Send 5
4,4
A
Steal 5
Pay 5
7,3
B
Take 6
Send 6
5,5
A
Steal 6, payoff 8,4
Pay 6, payoff 6,6
Example 6: Simple Humans
Centipede Game: Should Blockbuster send the first DVD to Albert? In
the rollback solution, Albert will steal the first DVD and terminate
the relationship. So Blockbuster should not send the first DVD.
But humans like Albert might not follow the rollback solution
because that solution is too conceptually complex. Rather, Albert
might pay for the first few DVDs, then plan to steal one of the last
DVDs. And as long as Albert pays for at least 2 DVDs before stealing,
Blockbuster makes positive profit.
Simultaneous move games

The Prisoners’ dilemma is whether or not to confess.

If you don’t confess, you get 1 year if the other prisoner does not confess and
15 years if he does.

If you do confess, you get 0 if the other prisoner does not confess and 5 years
if he does.

To decide whether to confess, define the normal form for the Prisoners’
Dilemma, and find any dominate strategies.
Prisoners’ dilemma
Confess is a dominate strategy for each prisoner. In
particular, it is the only Nash equilibrium.
Prisoner 2
Don't C.
Prisoner 1
Confess
Don't C.
-1,-1
0,-15
Confess
-15,0
-5,-5
Strategies

A dominant strategy for a player gives better payoffs for that player compared with
any other strategy, no matter what other players choose for their strategies.

A weakly dominant strategy for a player gives at least as good payoffs for that player
compared with any other strategy, no matter what other players choose for their
strategies, and better payoffs for at least one choice of strategies for the other
players.

A dominated strategy for a player gives worse payoffs for that player compared with
some other strategy, no matter what other players choose for their strategies.

While dominant strategies are the recommended choice to play games, dominated
strategies should never be chosen. Eliminating dominated strategies reduces the
game, and the new game may have further dominated strategies, which can be
eliminated, and so on.

A weakly dominated strategy for a player gives at least as bad payoffs for that player
compared with some other strategy, no matter what other players choose for their
strategies, and worse payoffs for at least one choice of strategies for the other players.

Eliminating weakly-dominated strategies reduces the game, and the new game may
have further weakly-dominated strategies, which can be eliminated, and so on.