1. The Theory of Individual Economic Behavior (Ch. 4)
Unit 3.
The Theory of Individual
Economic Behavior (Ch. 4)

2. Budget Constraint
The maximum Q combinations of goods that can be purchased given one’s income and the prices of the goods.

3. 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

4. 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

5. The Opportunity Set

6. 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

7. Budget Line Slope
Equation:
¯Slope = ¯
rate at which y CAN be exchanged for x (holding $ expenses constant) =
e.g.
=> 2y can be exchanged for 1x

8. 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.

9. 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.

10. Your Preferences? A: 1 drink, 1 pizza slice A: 1 movie, 1 dinner Lunch
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

11. 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)

12. An Understanding of Concepts Related to Indifference Curves and 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.

13. 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

14. 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.

15. Indifference Curve Analysis
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.

16. Investment Alternatives
Fund
Return
Safety A
2.89% Hi B
6.59%
Med C
7.29%
Low

18. 1. Ida Dontcare is indifferent regarding all three investment alternatives.
U(A) = U(B) = U(C)

19. 2. Ralph Returnman prefers C over B and prefers B over A.
U(C) > U(B) > U(A)

20. 3. Sally Safetyfirst prefers A over B and prefers B over C.
U(A) > U(B) > U(C)

21. 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

22. Indifference Curve Shape
Slope = MRS = marginal rate of substitution =
Rate at which consumer is willing
to exchange y for x = ΔY/ΔX
Two ways to calculate:
1) Given utility function equation, derive inverse MU ratio =

23. => Willing to exchange 2y for 1x
2) Given indifference curve equation, derive ¯dy/dx directly.
e.g. 1) 2)
=> Willing to exchange 2y for 1x

24. Types of Goods & Utility Functions
Normal
Perfect Substitutes
Perfect Complements

26. 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

27. Perfect Substitutes (= a constant)
= 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)

28. 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

29. Non ‘Goods’ & Indifference Curves
1 Good and 1 ‘Neutral’
1 Good and 1 ‘Bad’

30. 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

31. Consumer Equilibrium (U Max)
The equilibrium
consumption
bundle is the
affordable bundle
that yields the
highest level of satisfaction.

32. Equal Slopes Condition (for consumer equilibrium)
MUX/MUY = PX/PY
MUX/PX = MUY/PY

33. Consumer Equilibrium (Perfect Substitutes)

34. Consumer Equilibrium (Perfect Complements)

35. Changes in Price Substitute Goods Complementary 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.

36. Complementary Goods

37. Changes in Income Normal Goods Inferior 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.

38. Normal Goods

39. Figure An increase in the price of good X leads to a substitution effect (A to B) and an income effect (B to C).
Substitution effect – The movement along a given indifference curve that results
from a change in the relative prices of goods, holding real income constant.
Income effect – The movement from one indifference curve to another that results
from the change in real income caused by a price change.

40. 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.

41. 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.

42. A Classic Marketing Application

43. 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

44. Constraint: expenses = income CQ = N + PW  Q = (N + 24P)/C – (P/C)L
If C = 1,
Q = (N + 24P) - PL

45. 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

46. 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 $.

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

48. Intertemporal Choice Problem Graph