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 expenses-paid 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/PYI/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 SlopeEquation: y

I

P

P

PX

y

x

y

¯Slope = ¯ dydx

P

Pinverse P ra tiox

y

= rate at which y rate at which y CANCAN be exchanged for x be exchanged for x (holding $ expenses constant)(holding $ expenses constant)

e.g. P

P

y

xx

y

$ 1 0

$ 5

2

1

=> 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 counter-

clockwise.

- An increase rotates the budget

line clockwise.

Y

X

New Budget Line fora price decrease.

Your Preferences?• Lunch

A: 1 drink, 1 pizza sliceB: 1 drink, 2 pizza slicesC: 2 drinks, 1 pizza slice

• EntertainmentA: 1 movie, 1 dinnerB: 1 movie, 2 dinnersC: 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)

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

2) Given indifference curve equation, derive ¯dy/dx directly.e.g.

1)

2)

=> Willing to exchange 2y for 1x

MU

MUx

y

Two ways to calculate:

1) Given utility function equation, derive inverse MU ratio =

u x yMU

MU

y

xx

y

2 12

1

y U xdy

dx

2

2

1

Types of 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

dy

dx

MU

MU

x y

B x y

Y

BXx

y

B

B

1

1

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 BBX

_

/

dy

dxM RS

MU

MU Bx

y

(= 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’1 Good and 1 ‘Bad’

Utility MaximizationWords 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 bundlethat 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 = hrs/day worked (labored)

• L = hrs/day leisured (happy)

Note: L = 24 – W

• P = hourly wage or ‘pay’ rate

• Q = consumer good quantity

• C = price per unit of Q

• N = 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

II

l rP C

P C

l r

II

l rC

C

l rassum e P P

C I l r I l r C

01

0 01 1

01

01

0 1

1 0 1 0

1

( ) ( )

( ) ( )

( ) ( )

Intertemporal Choice Problem Graph