Download Unit 3.

Unit 3.
The Theory of Individual
Economic Behavior (Ch. 4)
Raise the Wage or Pay Overtime?
Boxes, Inc. produces corrugated paper containers at its
plant in Sunrise Beach, TX. The plant is located in a
retirement community with an aging population and a
shrinking work force which has hampered the firm’s
ability to hire enough workers to meet its growing
production targets. This is despite the fact that the
company already pays a wage rate that is twice the local
average. The firm’s manager is considering two options
to deal with the firm’s growing labor shortage: 1) raise
the wage rate by 50% to be paid for all hours worked by
workers or 2) implement an overtime wage plan that
would raise the wage rate by 50% to be paid for hours
worked in excess of 8 hours per day. Which plan would
you recommend?
Preferred Investment Strategy?
Bill is a financial planner for FVS (Financial
Vision Services’). Today, he has a meeting
scheduled with a client to discuss some
alternative retirement investment strategies. He
is trying to figure out which strategies the client
is most likely to be interested in. As he reviews
possible investment options, he is aware that
different strategies offer his client different risk
and return tradeoffs. Bill has decided to focus
on higher-returning (yet riskier) investments for
his client today, who is a middle-aged, white
collar worker. Do you agree with his approach?
Buy One, Get One Free
• A popular sales strategy of pizza
restaurants is to offer a deal “buy one
large pizza, get a medium pizza free”. Is
the budget impact of this strategy the
same as simply lowering the price of the
pizza? Which strategy would you
recommend to the manager of such a
restaurant to increase sales?
Cash or Vacation?
• Sue is a DSM (district sales manager) for a well
respected pharmaceutical company. She is
considering implementing a “bonus” plan to
provide additional incentive for sales reps to
reach sales goals. She has two alternative
bonus plans that she is looking at: 1) a straight
$2,000 cash bonus or 2) a $2,000 expensespaid vacation to a popular tourist attraction.
Which plan would you recommend Sue adopt,
without having any specific knowledge of her
sales reps?
What to Buy for a Snack?
• Molly Dogood is a grade-school student who has
a monthly allowance from her parents of $40 to
be spent on snacks at school. Molly is deciding
how much of her allowance to spend on S (=
cans of soda pop, $1.00 each) and O (other
items, prices vary). How can Molly’s attainable,
affordable choices be shown graphically and
mathematically? What combination of S and O
should Molly buy? When would Molly likely by
all S and no O?
Buying and Selling “Perfect”
Substitutes
• Assume two firms (A and B) compete against
each other by selling similar products in a
market. Currently, A’s product sells at a slightly
higher price. Jack is a prospective customer of
both. What does it mean if Jack regards the
products of A and B to be “perfect” substitutes. If
you were a sales rep working for either of these
firms, how would your sales pitch to Jack likely
depend on whether you work for A or B? When
would Jack likely buy either all A or all B?
I Save, You Borrow?
• Sonny and Cher have the same present
value of combined incomes this year and
next year. They also have the same
preferences regarding saving and
borrowing, yet Sonny is a saver and Cher
is a borrower. Explain how that can be?
Budget Constraint
 The maximum Q
combinations of goods that
can be purchased given one’s
income and the prices of the
goods.
Budget Constraint Variables
I (or M) =
the amount of income or money that a consumer
has to spend on specified goods and services.
X =
the quantity of one specific good or one specific bundle of
goods
Y =
the quantity of a second specific good or second specific
bundle of goods
Px =
the price or per unit cost of X
PY =
the price or per unit cost of Y
Budget Line Equation
• Income = expenses
• I = PxX+PYY
• Y = l/PY – (Px/PY)X
 straight line equation
 vert axis intercept = I/PY
 slope = dY/dX = -Px/PY
The Opportunity Set
Y
I/PY
Budget Line
PX
PY
I/PX
X
Budget Line: Axis Intercepts
& Slope
• Vertical Axis Intercept
=
=
I/PY
max Y (X = 0)
• Horizontal Axis Intercept
=
=
I/PX
max X (Y = 0)
• - Slope
= PX/PY
= ‘inverse’ P ratio
= X axis good P/Y axis good P
= Y/X
Budget Line Slope
Equation:
I Px
y

X
Py Py
¯Slope = ¯ dy  Px  inverse P ratio
dx
=
Py
rate at which y CAN be exchanged for x
(holding $ expenses constant)
e.g.
Px $10 2  y

 
Py $5 1  x
=> 2y can be exchanged for 1x
Changes in the Budget Line
• Changes in Income
-
Increases lead to a parallel,
outward shift in the budget line.
Decreases lead to a parallel,
downward shift.
Y
X
Changes in the Budget Line
• Changes in Price
-
-
A decrease in the price of good
X rotates the budget line counterclockwise.
An increase rotates the budget
line clockwise.
Y
New Budget Line for
a price decrease.
X
Your Preferences?
• Lunch
A:
B:
C:
1 drink, 1 pizza slice
1 drink, 2 pizza slices
2 drinks, 1 pizza slice
• Entertainment
A:
B:
C:
1 movie, 1 dinner
1 movie, 2 dinners
2 movies, 1 dinner
For each, indicate which of the following you prefer:
A vs B,
B vs C,
A vs C
Utility Concepts
• Utility:
satisfaction received from consuming goods
• Cardinal utility:
satisfaction levels that can be measured or specified
with numbers (units = ‘utils’)
• Ordinal utility:
satisfaction levels that can be ordered or ranked
• Marginal utility:
the additional utility received per unit of additional unit
of an item consumed (U/ X)
Different Types of Individual
‘Goods’
Inferior =>
Bad =>
Neutral=>
Normal=>
=>
∂Q/∂I < 0
MU < 0 (i.e. ∂U/∂X < 0)
MU = 0
MU > 0
∂Q/∂I > 0
An Understanding of Concepts Related to
Utility Should Help One:
1. Get along better with other people, by doing
things that increase their utility.
2. Make better business decisions that result in
improved customer satisfaction and, thus,
more sales.
3. Understand what motivates people and why
they behave the way they do, including how
people are likely to respond to economic
changes.
Utility Assumptions
1. Complete (or continuous)  can rank all
bundles of goods
2. Consistent (or transitive)  preference
orderings are logical and consistent
3. Consumptive (nonsatiation)  more of a
‘normal’ good is preferred to less
More of a Good is Preferred to
Less
The shaded area represents those combinations of X and Y that are
unambiguously preferred to the combination X*, Y*. Ceteris paribus,
individuals prefer more of any good rather than less. Combinations
identified by “?” involve ambiguous changes in welfare since they
contain more of one good and less of the other.
Indifference Curve Analysis
Indifference Curve
• A curve that defines the
combinations of 2 or more
goods that give a consumer
the same level of satisfaction.
Marginal Rate of Substitution
• The rate at which a consumer
is willing to substitute one good
for another and stay at the same
satisfaction level.
Investment Alternatives
Fund
Return
Safety
A
2.89%
Hi
B
6.59%
Med
C
7.29%
Low
1. Ida Dontcare is indifferent regarding
all three investment alternatives.
U(A) = U(B) = U(C)
2. Ralph Returnman prefers C over B and
prefers B over A.
U(C) > U(B) > U(A)
3. Sally Safetyfirst prefers A over B and
prefers B over C.
U(A) > U(B) > U(C)
MRS & MU
• MRS
= - slope of indifference curve
= -Y/ X
= the rate at which a consumer is willing to
exchange Y for 1more (or less) unit of X
U =
0 along given indiff curve
=
MUx(X)+MUY(Y) = 0
=
- Y/ X = MUx/MUY
=
- slope = inverse MU ratio
MRS Calculation
Two ways to calculate:
1) Given utility function equation, derive inverse MU ratio =
2) Given indifference curve equation, derive ¯dy/dx directly.
e.g.
1)
2)
MU x 2  y
u  2 x  1y 
 
MU y 1  x
 dy 2
y  U  2x 

dx 1
=> Willing to exchange 2y for 1x
MU x
MU y
Different Types of Relationships Between
Goods ( & Utility Functions)
1. Normal
2. Perfect Substitutes
3. Perfect Complements
Normal Goods
= goods for which a consumer’s willingness to
exchange one good for another varies
depending on Q’s of each
Represented by U = xαYB
 1 B
MU

dy

x
y
Y
x



 B 1 
dx
MU y B x y
BX
Perfect Substitutes
= goods for which a consumer is willing to
exchange one good for another at a constant
rate.
 Represented by U = αx + BY

Equation of indifferent curve = Y  U / B 
X
B
_
MU x 
 dy
 MRS 

dx
MU y B
(= a constant)
Perfect Complements
= goods that are used in fixed or constant
proportions with one another
Represented by U = min [αX, βY]
A consumer’s U = whichever is the least, αX
or βY
 too much of one good without more of the
other good will not increase one’s utility
 values where αX = βY lie along line (solve for
Y) where Y = (α/β)X
Non ‘Goods’ & Indifference Curves
 1 Good and 1 ‘Neutral’
1 Good and 1 ‘Bad’
Utility Maximization
Words
Spend one’s income so as to get the most satisfaction
possible
Graph
Go to the highest indifference curve that is within reach of
the budget line
Math
Normal goods: point of tangency (equal slopes condition)
between budget line and highest attainable indifference
curve
Perfect substitutes: corner solution normally; if slope of
budget line flatter than slope of indifference curves => All
X; else => All Y
Perfect complements; pt. of intersection between budget
line and line through vertex pts of indifference curves
Consumer Equilibrium
(U Max)
• The equilibrium
consumption
bundle is the
affordable bundle
that yields the
highest level of
satisfaction.
Equal Slopes Condition
(for consumer equilibrium)
• MUX/MUY = PX/PY
• MUX/PX = MUY/PY
Consumer Equilibrium
(Perfect Substitutes)
Consumer Equilibrium
(Perfect Complements)
Changes in Price
• Substitute Goods
– An increase (decrease) in the price of good
X leads to an increase (decrease) in the
consumption of good Y.
• Complementary Goods
– An increase (decrease) in the price of good
X leads to a decrease (increase) in the
consumption of good Y.
Complementary Goods
Changes in Income
• Normal Goods
– Good X is a normal good if an increase (decrease) in
income leads to an increase (decrease) in its
consumption.
• Inferior Goods
– Good X is an inferior good if an increase (decrease)
in income leads to a decrease (increase) in its
consumption.
Normal Goods
Individual Demand Curve
• An individual’s
demand curve is
derived from each
new equilibrium
point found on the
indifference curve as
the price of good X
is varied.
Market Demand
• The market demand curve is the horizontal
summation of individual demand curves.
• It indicates the total quantity all consumers
would purchase at each price point.
A Classic Marketing Application
Variables:
• W =
• L =
•
•
•
•
P
Q
C
N
=
=
=
=
hrs/day worked (labored)
hrs/day leisured (happy)
Note: L = 24 – W
hourly wage or ‘pay’ rate
consumer good quantity
price per unit of Q
nonlabor income
Constraint:
expenses = income
CQ = N + PW
 Q = (N + 24P)/C –
(P/C)L
If C = 1,
Q = (N + 24P) - PL
Intertemporal Choice Model
• Inter  between; temporal  time pds
• Time pds  current (0) or next yr (1)
Variables:
C0 and C1 = Q of goods consumed
I0 and I1 = income levels
P = price of consumer goods (P0 = P1)
r = interest rate
• Objective (goal) = Max U = f(C0, C1)
• Constraint: PV of Income = PV of Expenses
Intertemporal Saving &
Borrowing Facts
• If you save an extra $ (i.e. reduce current
pd consumption by a $), you can
INCREASE future pd consumption by the
FV of the $.
• If you borrow a $ against your future
income (i.e. agree to pay back a $
principal and interest), you can
INCREASE current pd consumption by the
PV of the $.
Math Summary of Intertemporal
Choice Problem
• Max U (C0, C1)
• Subj. to PV of income = PV of expenses
I1
P1C1
I0 
 P0 C0 
(l  r )
(l  r )
I1
C1
I0 
 C0 
assume P0  P1  1
(l  r )
(l  r )
C1  I 0 (l  r )  I 1  (l  r ) C0
Intertemporal Choice Problem
Graph
NET SAVER
C1
U*
I1
C0
I0
NET BORROWER
C1
I1
U*
I0
C0