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Unit 3. The Theory of Individual Economic Behavior (Ch. 4). Raise the Wage or Pay Overtime?.

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unit 3

Unit 3.

The Theory of Individual

Economic Behavior (Ch. 4)

raise the wage or pay overtime
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
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
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
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
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
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
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
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
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
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

budget line axis intercepts slope
Budget Line: Axis Intercepts & Slope
  • Vertical Axis Intercept

= I/PY

= max Y (X = 0)

  • Horizontal Axis Intercept

= I/PX

= max X (Y = 0)

  • - Slope


= ‘inverse’ P ratio

= X axis good P/Y axis good P

= Y/X

budget line slope
Budget Line Slope


¯Slope = ¯

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



=> 2y can be exchanged for 1x

changes in the budget line
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.

changes in the budget line1
Changes in the Budget Line
  • Changes in Price

- A decrease in the price of good

X rotates the budget line counter-


- An increase rotates the budget

line clockwise.

your preferences
Your Preferences?
  • Lunch

A: 1 drink, 1 pizza slice

B: 1 drink, 2 pizza slices

C: 2 drinks, 1 pizza slice

  • Entertainment

A: 1 movie, 1 dinner

B: 1 movie, 2 dinners

C: 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 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
An Understanding of Concepts Related to Utility Should Help One:
  • Get along better with other people, by doing things that increase their utility.
  • Make better business decisions that result in improved customer satisfaction and, thus, more sales.
  • Understand what motivates people and why they behave the way they do, including how people are likely to respond to economic changes.
utility assumptions
Utility Assumptions
  • Complete (or continuous)  can rank all bundles of goods
  • Consistent (or transitive)  preference orderings are logical and consistent
  • Consumptive (nonsatiation)  more of a ‘normal’ good is preferred to less
more of a 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 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.

1 ida dontcare is indifferent regarding all three investment alternatives
1. Ida Dontcare is indifferent regarding all three investment alternatives.

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
MRS Calculation

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




=> Willing to exchange 2y for 1x

Two ways to calculate:

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

types of goods utility functions
Types of Goods & Utility Functions
  • Normal
  • Perfect Substitutes
  • Perfect Complements
normal goods
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
perfect substitutes
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 =

(= a constant)

perfect complements
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
Non ‘Goods’ & Indifference Curves
  • 1 Good and 1 ‘Neutral’
  • 1 Good and 1 ‘Bad’
consumer equilibrium u max
Consumer Equilibrium (U Max)
  • The equilibrium


bundle is the

affordable bundle

that yields the

highest level of satisfaction.

changes in price
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.
changes in income
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.
individual demand curve
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
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.
  • 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
  • expenses = income
  • CQ = N + PW

 Q = (N + 24P)/C – (P/C)L

If C = 1,

Q = (N + 24P) - PL

intertemporal choice model
Intertemporal Choice Model
  • Inter  between; temporal  time pds
  • Time pds  current (0) or next yr (1)


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
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
Math Summary of Intertemporal Choice Problem
  • Max U (C0, C1)
  • Subj. to PV of income = PV of expenses