budget line and indifference curve

1. Household behavior
&
Consumer choice
Prepered by
Dr.Mohamed Osman
Lecturer of public economics faculty of commerce-Alexandria
University

2. First: The Basic of Choice: Utility
*Utility: is the satisfaction received from
consuming any good.
*Total utility (TU)
Is the total amount of satisfaction received
from consuming a given amount of a good.
*Marginal utility (MU)
Is the additional satisfaction received from
consuming one more unit of a good.

3. Example:
Given the following table showing the (MU)
received from consuming good (x) . Calculate
the TU & show graphically the MU & TU
curves.
7654321Q
32343431261910Tux.

4. Answer
7654321Q
32343431261910TUx.
-20357910MUx.

5. TU
MU
Diminishing MU
Qx
Qx
Maximum TU
TU curve
Zero
Negative MU

6. NOTES:-
*TU is increasing at a decreasing rate, in other
word, TU is increasing by smaller and smaller
amount for each additional unit.
*MU curve is downward sloping because
consumption of successive units gives less
satisfaction.
*When TU is increasing → Diminishing MU.(MU is positive).
*When TU reaches maximum → MU reaches zero.
*When TU is decreasing →MU is negative.

7. • Law of diminishing marginal utility:
The more of any good is consumed, the less the
utility (satisfaction) obtained from consuming
each additional unit from this good.
(as Q consumed ↑ →MU ↓)

9. Indifference curves theory
-The theory of indifference curves seeks to
answer the following question:-
HOW CAN CONSUMER MAXIMIZE HIS UTILITY
GIVEN HIS INCOME & THE PRICE OF GOODS?
*The consumer’s income & the price of goods
are represented by ( the budget line )
*the consumer’s utility or satisfaction is
represented by ( the indifference )

10. 1-Budget line
Definition & Graph of the budget line:
The budget constraint or line (B.L) shows all
combinations of two goods that can be
purchased with a given income & given
prices.

11. -Graph of budget line:-
the following table shows all combinations of
two goods ( X&Y ) that can be purchased with
a given income(I)= 20 & given prices ( Px=4 &
Py=2).
YXCombinations
100A
81B
62C
43D
24E
05F

12. Y
X
2
4
6
8
10
12
1 2 3 4 5 6
.B
.C
.D
.E
A
F

13. • Note:-
1-We can draw the budget line by knowing 2
points only (A&F) :-
-A……. The maximum quantity of Y=
-F…….. The maximum quantity of X=

14. 2-
*Points on B.L :
all attainable combinations &
income is fully spent
*Points below B.L :
are attainable combination but
income is not fully spent
*Points above B.L :
are unattainable combination
(it cannot be purchased)

15. Slope & Equation of the budget constraint

16. The effect of income on the budget line:-
• If I BL shifts up.( slope is constant )
• If I BL shifts Down.( slope is constant )
EX:-
-In the previous example if the
income rises to 40.
-The maximum quantity of Y= = 20
-The maximum quantity of X= =10
-In the previous example if the
income falls to 10.
-The maximum quantity of Y= = 5
-The maximum quantity of X= =2.5

17. The effect of price change on the budget line
-If Px OR Py ……. BL rotates down (BL becomes steeper) .
-If Px OR Py ……. BL rotates up (BL becomes flatter) .

18. EX:-
-In the previous example if
*I =20.
*Px rises to 5
*Py = 2
-The maximum quantity of Y= = 10
-The maximum quantity of X= = 4

19. EX:-
-In the previous example if
*I =20.
*Px falls to 2
*Py = 2
-The maximum quantity of Y= = 10
-The maximum quantity of X= = 10

20. EX:-
-In the previous example if
*I =20.
*Px = 4
*Py rises to 4
-The maximum quantity of Y= = 5
-The maximum quantity of X= = 5

21. EX:-
-In the previous example if
*I =20.
*Px = 4
*Py falls to 1
-The maximum quantity of Y= = 20
-The maximum quantity of X= = 5

22. NOTES:-
1- If both prices increase by the same percentage,
the BL will shift downward & vice versa.
2- If income and both prices increase by the same
percentage, BL will not be affected.
3- Δ in income has no effect on the slope of B.L.
4- Δ Of price of one good affect on the slope of B.L

23. Example:
If income (I) = 100 Px = 2 Py = 5
1) Draw the B.L using numbers above?
2) Calculate the slope of B.L?
3)what's the equation of B.L ?
4) If combination (A) on the B.L shows that the consumer
buys 30 units of good. x calculate the quantity of y.
5)shows graphically the effect of a rise in income to 200 on
the B.L
6)shows graphically the effect of a fall in Px to 1 on the B.L

26. 2-Indifference Curves
Definition & Graph:-
• The indifference curve shows all
combinations of the two goods that are
equally desirable to the consumer (that given
to consumer the same satisfaction).

27. -Example:- Suppose that 4
combinations of two
goods (Y&X) that given
to consumer the same
satisfaction.
XYCombination
16A
23B
32C
41.5D
Y
X
1
2
3
4
5
6
1 2 3 4 5 6
.A
.B
.C
.E
Indifference curve

28. • Points lying along the
same I.C such as (a ,b ,c)
are equally preferred
(give same satisfaction)
• Points on the higher I.C
are preferred to any
point on a lower I.C
(give higher satisfaction
to the consumer).
ex: comb. (e) is preferred
to comb. (d)

29. Slope Of indifference Curve
*The slope of I.C is the marginal
rate of substitution (MRS)
which measure " what must
be given up from one good to
get additional unit of the
other good in order to keep
satisfaction constant .
Slope of I.C=MRS = = -
MUx=Marginal utility of x derived
from consuming the last unit of x.
Muy=Marginal utility of y derived
from consuming the last unit of y.
.
MRSXYcombinations
-16A
-3:123B
-1:132C
-0.5:141.5D

30. Characteristics of Indifference curves
1- IC is negatively (downward) slope
• As the level of satisfaction is constant along
the IC, having more of one good require
having less of the other good (-ve relation).

31. 2- ICs cannot intersect:-
-(a) = (b) (same IC:IC1)
-(a) =(c) (same IC:IC2)
-So (b) Must equal (c)
but actually (c) is better
than (b) because it lies
on a higher IC
-So ICs cannot intersect

32. 3- IC is "bowed in" (or convex)
because of diminishing MRS
Any consumer is willing to
sacrifice less & less unit
from one good for
additional unit of the other
good (MRS is decreasing )
which requires a convex IC
to show this characteristics
.The previous example shows
diminishing MRS
MRS (slope of IC) is decreasing
along the convex IC
Y
X
1
2
3
4
5
6
1 2 3 4 5
Indifference curve

33. Consumer utility – maximizing equilibrium
(The Optimal Consumer Choice)
• The consumer will get the maximum utility
from his income at the point of tangency
between the budget line & the highest
attainable indifference

34. -At the point of tangency:-
*Slope Of IC = Slope of B.L
MRS = -
- = -
=
*From the last equation the utility
maximizing rule states that consumer
maximize his utility by equating the
marginal utility per dollar spent on
x : with the marginal utility per
dollar spent on y:

35. Derivation of Consumer Demand Curve

36. Q1:-
-A consumer has an income of
2000$ which he spends on
goods X & Y given the follow
graph.
1-Drtermine Px & Py when the BL
is (ab).
2-Determine Px & Py when the BL
is (ac).
3-What are the quantities of y at
(E1) & (E2).
4- Determine the MRS at (E1) &
(E2).
5-Derive the demand curve for (x).
6-Are (x) & (y) substitutes or
complements?
• .
Y
X
40
.E2
.E1
5020 3010
a
b c

37. Q2-True or False
1- The two indifference curve never intersect.
2- When money income increase with no
change in price the budget line will rotate
outside.
3-The Consumers equilibrium point is the
intersection point between the budget line
and the highest indifference curve.
4-Indifference curve is convex to the origin
because MRS is increasing.