### A.6 Manipulating Others

```Readings
Baye 6th edition or 7th edition, Chapter 4
BA 445 Lesson A.6 Manipulating Others
1
Overview
Overview
BA 445 Lesson A.6 Manipulating Others
2
Overview
Consumer Optimum is when a consumer makes a rational choice (maximizes
happiness) subject to a budget constraint on money or time. — So, customers
optimize purchases and workers optimize leisure and work.
Gross Substitutes and Complements combine substitution and income effects of
a price increase for one good on the demand for another good. — So, they
explain the affect of higher-priced housing on cars.
Buy 1 Get 1 Free deals indirectly affect consumer optimum choices by
manipulating their budget sets. — So, firms can manipulate customers to buy
more.
Quantity Discounts manipulate customers’ budget sets. — So, firms can
manipulate customers to spend more while receiving less quantity.
Overtime Wages manipulate workers’ budget sets. — So, firms can manipulate
workers to receive less income while working more hours.
BA 445 Lesson A.6 Manipulating Others
3
Consumer Optimum
Consumer Optimum
BA 445 Lesson A.6 Manipulating Others
4
Consumer Optimum
Overview
Consumer Optimum is when a consumer makes a rational
choice (maximizes happiness) subject to a budget
constraint on money or time. — So, customers optimize
purchases and workers optimize leisure and work.
BA 445 Lesson A.6 Manipulating Others
5
Consumer Optimum
Consider definitions for a simple
budget constraint. Apples cost \$3
each, oranges \$4 each, and
consumer income is \$24.
• Budget Set is the triangular set of
consumption bundles of apples
and oranges that are affordable:


Budget Line
6
Y = 6 – (3/4)X
3X + 4Y  24
• Budget Line is the line of bundles
that exhaust income:

Y
Budget Set
3X + 4Y = 24
Or, Y = 6 – (3/4)X
8
X
• Market Rate of Substitution is the
slope of the budget line: -3/4
BA 445 Lesson A.6 Manipulating Others
6
Consumer Optimum
More generally, consider any two
goods selling at positive prices Px
Y
and Py, and consumer income M.
• Budget Set is the triangular set of
consumption bundles of goods X M/P
and Y that are affordable:
Y

Budget Line
Y = M/PY – (PX/PY)X
PxX + PyY  M
• Budget Line is the line of bundles
that exhaust income:


PxX + PyY = M
Or, Y = M/PY – (PX/PY)X
Budget Set
• Market Rate of Substitution is the
slope of the budget line: -Px / Py
BA 445 Lesson A.6 Manipulating Others
M/PX
X
7
Consumer Optimum
Y
Graph changes in budget lines M /P
as parameters change:
M /P
• Changes in Income:


outward shift in the budget
line (M1 > M0).
inward shift (M2 < M0).
• Changes in Price:


1
Y
0
Y
M2/PY
Y
M0/PY
Decreases in the price of
good X rotates the budget line
counter-clockwise (PX0 > PX1).
Increases in the price of good
X rotates the budget line
clockwise (not shown).
M2/PX
M0/PX
M0/PX0
BA 445 Lesson A.6 Manipulating Others
M1/PX
M0/PX1
X
X
8
Consumer Optimum
Consumer Optimum is when
a consumer makes a rational
choice (maximizes
happiness) subject to a
budget constraint.
• Consumer optimum occurs
where the slope of the
indifference curve equals
the slope of the budget
line.
• The Consumer would be
happier with more
consumption than the
optimum, but that is
unaffordable (it violates the
budget constraint).
Y
Happier
M/PY
Happy
Consumer
Optimum
BA 445 Lesson A.6 Manipulating Others
M/PX
X
9
Consumer Optimum
Normal Goods have
increased consumption
caused by an income
increase.
• Examples include
steak, cars…
• The movement from A
to B is caused by an
income increase.
• Since the consumption
of both goods
increases, both goods
are normal.
Y
M1/PY
B
Y1
M0/PY
A
Y0
0
X0 M0/PX
X1
BA 445 Lesson A.6 Manipulating Others
M1/PX
X
10
Consumer Optimum
Inferior Goods have
decreased consumption
caused by an income
increase.
• Examples include hot
dogs, economy cars, …
• The movement from A
to B is caused by an
income increase.
• Since the consumption
of good X decreases
and good Y increases,
good X is inferior and
good Y is normal.
Y
M1/Y
B
M0/Y
A
Y0
0
X0 M0/PX
BA 445 Lesson A.6 Manipulating Others
M1/PX
X
11
Gross Substitutes and Complements
Gross Substitutes and
Complements
BA 445 Lesson A.6 Manipulating Others
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Gross Substitutes and Complements
Overview
Gross Substitutes and Complements combine substitution
and income effects of a price increase for one good on the
demand for another good. — So, they explain the affect of
higher-priced housing on cars.
BA 445 Lesson A.6 Manipulating Others
13
Gross Substitutes and Complements
Definitions for the effects of a price change
• Gross Substitutes
 An increase in the price of good X leads to an
increase in the consumption of good Y.
• Examples:
– Coke and Pepsi.
– Verizon Wireless or AT&T.
– Beer and wine.
• Gross Complements
 An increase in the price of good X leads to a
decrease in the consumption of good Y.
• Examples:
– DVD and DVD players.
– Computer CPUs and monitors.
– Beer and pretzels.
BA 445 Lesson A.6 Manipulating Others
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Gross Substitutes and Complements
Graphing Gross Substitute Goods
When the price of
Wine (Y)
good X falls
(PX1 > PX2) and
the consumption
of Y falls, then X
and Y are gross
substitute goods.
M/PY1
A
Y1
B
Y2
I
0
X1 M/PX1
II
X2
BA 445 Lesson A.6 Manipulating Others
M/PX2
Beer (X)
15
Gross Substitutes and Complements
Graphing Gross Complement Goods
When the price of
Pretzels
good X falls
(Y)
(PX1 > PX2) and
M/PY1
the consumption
of Y rises, then X
and Y are gross
complement
goods.
Y2
B
II
A
Y1
I
0
X1 M/PX1
X2
BA 445 Lesson A.6 Manipulating Others
M/PX2
Beer (X)
16
Gross Substitutes and Complements
Decomposition into Substitution and Income Effects
• An increase in the price of Good X causes both a substitution effect
and an income effect.
• The substitution effect concerns finding the cheapest way to meet
your needs (happiness, nutrition, …). Goods are
•
•
substitutes if an increase in price of X increases demand for Y
complements if an increase in price of X decreases demand for Y
• The income effect concerns adjusting consumption to what you can
afford. An increase in the price of Good X first causes a decrease in
any good.
•
•
If Good Y is normal, then an increase in the price of Good X first
causes a decrease in purchasing power, which then decreases
demand for Y.
If Good Y is inferior, then an increase in the price of Good X first
causes a decrease in purchasing power, which then increases demand
for Y.
BA 445 Lesson A.6 Manipulating Others
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Gross Substitutes and Complements
Why not use the simplified definition of Substitutes and
Complements?
• Recall the simplified definition from an Introduction to
Microeconomics is Good X and Good Y are
•
•
substitutes if an increase in price of X increases demand for Y
complements if an increase in price of X decreases demand for Y
• There are examples when that definition makes sense:
•
Apples and oranges: An increase in price of apples increases demand
for oranges since consumers switch from one fruit to the cheaper fruit.
• Sometimes that definition makes no sense:
•
•
Pepperdine and oranges: An increase in tuition at Pepperdine
decreases demand for oranges since consumers can no longer afford
fruit. Would you say Pepperdine and oranges are complements?
Pepperdine and Raman noodles: An increase in tuition at Pepperdine
increases demand for noodles since consumers can no longer afford
other food. Would you say Pepperdine and noodles are substitutes?
BA 445 Lesson A.6 Manipulating Others
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Gross Substitutes and Complements
The Gross definition always makes sense
• Example: Apples and oranges. An increase in price of
apples increases demand for oranges in the substitution
effect since consumers switch from one fruit to the
cheaper fruit. But the increase in the price of apples
causes only a small income effect. So the substitution
effect dominates. Apples and oranges are substitutes
and gross substitutes.
BA 445 Lesson A.6 Manipulating Others
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Gross Substitutes and Complements
The Gross definition always makes sense
• Example: Pepperdine and oranges.
• An increase in tuition at Pepperdine causes only a small
substitution effect on oranges since the two goods do not
substitute or complement each other (not like Pepperdine and
books, or Pepperdine and computers).
• An increase in tuition at Pepperdine causes a large decrease in
purchase any good, including oranges.
• So increase in tuition at Pepperdine decreases demand for
oranges. Call the Pepperdine and oranges gross complements
since the demand decrease for the second good is the
combination of both the substitution effect and the income effect.
BA 445 Lesson A.6 Manipulating Others
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Gross Substitutes and Complements
The Gross definition always makes sense
• Example: Pepperdine and Raman noodles.
• An increase in tuition at Pepperdine causes only a small
substitution effect on Raman noodles since the two goods do
not substitute or complement each other (not like Pepperdine
and books, or Pepperdine and computers).
• An increase in tuition at Pepperdine causes a large decrease in
purchase any good and the need to buy cheaper goods, like
Raman noodles.
• So increase in tuition at Pepperdine increases demand for
Raman noodles. Call the Pepperdine and Raman noodles
gross substitutes since the demand increase for the second
good is the combination of both the substitution effect and the
income effect.
BA 445 Lesson A.6 Manipulating Others
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Gross Substitutes and Complements
The Gross definition always makes sense
• Example: SoCal housing and cars:
• An increase in SoCal housing causes only a small substitution
effect on cars since the two goods do not substitute or
complement each other (not like SoCal housing and furniture, or
SoCal housing and Arizona housing).
• An increase in price for SoCal housing causes a large decrease
purchase any good, including cars.
• So increase in price for SoCal housing decreases demand for
cars. Call the SoCal housing and cars gross complements
since the demand decrease for the second good is the
combination of both the substitution effect and the income effect.
BA 445 Lesson A.6 Manipulating Others
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BA 445 Lesson A.6 Manipulating Others
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Overview
Buy 1 Get 1 Free deals indirectly affect consumer
optimum choices by manipulating their budget sets. —
So, firms can manipulate customers to buy more.
BA 445 Lesson A.6 Manipulating Others
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• Why does Little Caesars Pizza offer two pizzas for the
price of one? For example, buy one pizza for \$10, get
one pizza free.
• Might some consumers be attracted by the idea of free
is an unplanned decision to buy a product or service,
• Have you ever enjoyed making a carefree impulse
• Or, do you always satisfy economic assumptions and
consider how a deal affects your budget set?
• Is “buy one pizza for \$10 get one pizza free” the same as
BA 445 Lesson A.6 Manipulating Others
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Buy one, get one free analysis: This deal
can get customers to buy more pizza than
cutting price in half. Consider budget
lines and choices when Pizzas cost \$10,
all other goods cost \$1 each, customer
income is \$30, and sample indifference
curves I (sad) and II (happy).
30
With no deal (Pizza cost remains \$10),
• Budget line connects (3,0) and (0,30)
With buy one, get one free (Pizza cost \$10)
20
• Budget line segments connect (0,30), (1,20),
(2,20), and (4,0)
• Consumption A, with 2 Pizzas
• Happiness level I.
With half price (Pizza cost \$5),
• Budget line has connects (6,0) and (0,30).
0
• Consumption bundle B, with 1 pizza.
• Happiness level II.
All other goods
B II
A
I
1
2
3
4
Pizzas (in continuous units)
BA 445 Lesson A.6 Manipulating Others
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Quantity Discounts
Quantity Discounts
BA 445 Lesson A.6 Manipulating Others
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Quantity Discounts
Overview
Quantity Discounts manipulate customers’ budget
sets. — So, firms can manipulate customers to spend
more while receiving less quantity.
BA 445 Lesson A.6 Manipulating Others
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Quantity Discounts
• We considered buy one get one free, and showed
how consumers can choose to consume more but be
less happy than if price were reduced.
• Buy X get Y free can likewise cause consumers to
consume more but be less happy. Consider a frequentflyer program of buy 8 flights get 1 flight free.
BA 445 Lesson A.6 Manipulating Others
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Quantity Discounts
Buy one get the rest at half price can be even more
effective for producers. When compared with reducing the
price by half for all units, “buy one get the rest at half price”
can cause consumers to
• Consume less of the good
• Spend more on the good
BA 445 Lesson A.6 Manipulating Others
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Quantity Discounts
Buy one, get rest at half price analysis:
This deal can get customers to spend
more on less pizza than cutting the price
for all units. Consider Pizza cost \$10, all
other goods cost \$1 each, customer
income is \$30, and sample indifference
curves I (sad) and II (happy).
30
With no deal (Pizza cost \$10),
• Budget line connects (0,30) and (3,0)
With buy one, get rest at half (Pizza cost \$10
20
for first, then \$5 for rest)
• Budget line segments connect (0,30), (1,20),
and (5,0)
• Consumption A, with 2 Pizzas
• Consumer spends \$15
With half price (Pizza cost \$5 for each),
0
• Budget line has intercepts (0,30) and (6,0).
• Consumption bundle B, with 2.5 pizzas.
• Consumer spends \$12.5
All other goods
B
A
II
I
2
1
3
4
Pizzas (in continuous units)
BA 445 Lesson A.6 Manipulating Others
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Overtime Wages
Overtime Wages
BA 445 Lesson A.6 Manipulating Others
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Overtime Wages
Overview
Overtime Wages manipulate workers’ budget sets. —
So, firms can manipulate workers to receive less
income while working more hours.
BA 445 Lesson A.6 Manipulating Others
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Overtime Wages
Buy one get the rest at half price or buy X get the rest at
half price can be adapted to employees as overtime wages.
The program is to offer work 8 hours a day at the normal
wage rate and work hours beyond 8 at double the normal
wage. The results of those overtime wages are similar to
buy one get the rest at half price. When compared with
doubling the wage for all hours worked, “work 8 hours at
the normal wage and work the rest at double wages” can
cause employees to
• Work more hours
BA 445 Lesson A.6 Manipulating Others
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Overtime Wages
Overtime wage analysis: Employees have
24 hours per day to divide between
leisure and work. Employees consume
leisure and “all other goods”. Consider
All goods other than
normal wage \$10, all other goods cost \$1
leisure
each, and sample indifference curves I
480
With no deal (wages \$10),
• Budget line connects (0,240) and (24,0)
400
Work 8, work rest at double wage (wages \$10
for first 8 hours, then \$20 for rest)
240
B
• Budget line segments connect (0,400),
(16,80), and (24,0)
II
A
I
• Consumption A, with leisure 11 and work 13 80
• Consumer earns \$180 = \$10x8 + \$20x5
With double wage (wages \$20),
11 13 16
0
24
• Budget line has intercepts (0,480) and (24,0)
Leisure hours (in continuous units)
• Consumption B, with leisure 13 and work 11
• Consumer earns \$220 = \$20x11
BA 445 Lesson A.6 Manipulating Others
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Review Questions
Review Questions
 You should try to answer some of the review
questions (see the online syllabus) before the next
class.
request to discuss their answers to begin the next class.
 Your upcoming Exam 1 and cumulative Final Exam
will contain some similar questions, so you should
eventually consider every review question before taking