Budget Constraints - Otaru University of Commerceyamamoto/files/May_2.pdf©2005 Pearson Education, Inc. Chapter 3 1 Budget Constraints The Budget Line Indicates all combinations of

Chapter 3 1©2005 Pearson Education, Inc.

Budget Constraints

� The Budget Line�Indicates all combinations of two

commodities for which total money spentequals total income

�We assume only 2 goods are consumed, sowe do not consider savings


The Budget Line

� Let F equal the amount of foodpurchased, and C is the amount ofclothing

�Price of food = PF and price ofclothing = PC

� Then PFF is the amount of money spenton food, and PCC is the amount of moneyspent on clothing


ICPFPCF =+

The Budget Line

� The budget line then can be written:

All income is allocated to food (F) and/or clothing(C)


The Budget Line pp. 79 - 83

�Different choices of food and clothing canbe calculated that use all income�These choices can be graphed as the budget

line

�Example:�Assume income of $80/week, PF = $1 and PC

= $2


Budget Constraints pp. 79 - 83

$80080G

$801060E

$802040D

$803020B

$80400A

IncomeI = PFF + PCC

Clothing

PC = $2

Food

PF = $1

MarketBasket


Slope = ΔCΔF

= -12

= -PF

PC1F + 2C = 80


10

20

A

B

D

E

G

(I/PC) = 40

Food40 60 80 = (I/PF)20

10

20

30

0

Clothing



�As consumption moves along a budgetline from the intercept, the consumerspends less on one item and more on theother

� The slope of the line measures therelative cost of food and clothing

� The slope is the negative of the ratio ofthe prices of the two goods



� The slope indicates the rate at which thetwo goods can be substituted withoutchanging the amount of money spent

�We can rearrange the budget lineequation to make this more clear



YXP

P

P

I

YPXPI

YPXPI

Y

X

Y

YX

YX

=−

=−

+=



� 1F + 2C = 80

� C = -0.5F + 40


Budget Constraints pp. 79 - 83

� The Budget Line�The vertical intercept, I/PC, illustrates the

maximum amount of C that can bepurchased with income I

�The horizontal intercept, I/PF, illustrates themaximum amount of F that can bepurchased with income I



�As we know, income and prices canchange

�As incomes and prices change, there arechanges in budget lines

�We can show the effects of thesechanges on budget lines and consumerchoices


The Budget Line - Changes pp. 79 - 83

� The Effects of Changes in Income�An increase in income causes the budget

line to shift outward, parallel to the originalline (holding prices constant).

�Can buy more of both goods with moreincome

�How about when an income tax is raised?



An increase inincome shifts

the budget lineoutward

Food(units per week)

Clothing(units

per week)

80 120 16040

20

40

60

80

0

(I = $160)L2

(I = $80)L1

L3

(I =$40)

A decrease inincome shifts

the budget lineinward



� The Effects of Changes in Prices�If the price of one good increases, the

budget line shifts inward, pivoting from theother good’s intercept.

�If the price of food increases and you buyonly food (x-intercept), then you can’t buy asmuch food. The x-intercept shifts in.

�If you buy only clothing (y-intercept), you canbuy the same amount. No change in y-intercept.



� The Effects of Changes in Prices�If the price of one good decreases, the

budget line shifts outward, pivoting from theother good’s intercept.

�If the price of food decreases and you buyonly food (x-intercept), then you can buymore food. The x-intercept shifts out.

�If you buy only clothing (y-intercept), you canbuy the same amount. No change in y-intercept.



(PF = 1)

L1

An increase in theprice of food to$2.00 changesthe slope of thebudget line androtates it inward.L3

(PF = 2)(PF = 1/2)

L2

A decrease in theprice of food to$.50 changes

the slope of thebudget line and

rotates it outward.

40Food(units per week)

Clothing(units

per week)

80 120 160

40



� The Effects of Changes in Prices�If the two goods increase in price, but the

ratio of the two prices is unchanged, theslope will not change

�However, the budget line will shift inwardparallel to the original budget line

�Example: An increase in sales (Consumption)tax



� The Effects of Changes in Prices�If the two goods decrease in price, but the

ratio of the two prices is unchanged, theslope will not change

�However, the budget line will shift outwardparallel to the original budget line


Consumer Choice pp. 83 - 89

�Given preferences and budgetconstraints, how do consumers choosewhat to buy?

�Consumers choose a combination ofgoods that will maximize their satisfaction,given the limited budget available to them



� The maximizing market basket mustsatisfy two conditions:

1. It must be located on the budget line� They spend all their income – more is better

2. It must give the consumer the mostpreferred combination of goods andservices



�Graphically, we can see differentindifference curves of a consumerchoosing between clothing and food

�Remember that U3 > U2 > U1 for ourindifference curves

�Consumer wants to choose highest utilitywithin their budget



U3

D

U2

C

Food (units per week)40 8020

Clothing(units per

week)

20

30

40

0

U1

A

B

•A, B, C on budget line•D highest utility but notaffordable•C highest affordableutility•Consumer chooses C



�Consumer will choose highestindifference curve on budget line

� In previous graph, point C is where theindifference curve is just tangent to thebudget line

�Slope of the budget line equals the slopeof the indifference curve at this point



�Recall, the slope of an indifference curveis:

F

CMRS

Δ

Δ−=

C

F

P

PSlope −=

Further, the slope of the budget line is:



� Therefore, it can be said at consumer’soptimal consumption point,

C

F

P

PMRS =



� It can be said that satisfaction ismaximized when marginal rate ofsubstitution (of F and C) is equal to theratio of the prices (of F and C)

�Note this is ONLY true at the optimalconsumption point



� Optimal consumption point is where marginalbenefits equal marginal costs

� MB = MRS = benefit associated withconsumption of 1 more unit of food. Or, it showshow much you are willing to pay in units ofclothing for an additional unit of food (I.e., yoursubjective evaluation)

� MC = cost of additional unit of food�PF/PC (units of clothing you must give up in

exchange for an additional unit of food)



� If MRS � PF/PC then individuals canreallocate basket to increase utility

� If MRS > PF/PC

�Will increase food and decrease clothing untilMRS = PF/PC

� If MRS < PF/PC

�Will increase clothing and decrease food untilMRS = PF/PC



Food (units per week)

Clothing(units per

week)

40 8020

20

30

40

0

Point B does notmaximize satisfaction

because theMRS = -10/10 = 1

is greater than theprice ratio = 1/2

+10F U1

-10C

B


Consumer Choice:An Application Revisited pp. 83 - 89

�Consider two groups of consumers, eachwishing to spend $10,000 on the stylingand performance of a car

�Each group has different preferences



�By finding the point of tangency betweena group’s indifference curve and thebudget constraint, auto companies cansee how much consumers value eachattribute



Styling

Performance$10,000

$10,000 These consumerswant performance

worth $7000 and stylingworth $3000

$3,000

$7,000



These consumerswant styling worth

$7000 andperformance worth

$3000

$3,000

$7,000

Styling

$10,000

$10,000

Performance



�Once a company knows preferences, itcan design a production and marketingplan

�Company can then make a sensiblestrategic business decision on how toallocate performance and styling on newcars



�A corner solution exists if a consumerbuys in extremes, and buys all of onecategory of good and none of another�MRS is not necessarily equal to PA/PB


A Corner Solution pp. 83 - 89

Ice Cream (cup/month)

FrozenYogurt(cups

monthly)

B

A

U2 U3U1

A corner solutionexists at point B.



� At point B, the MRS of ice cream for frozenyogurt is greater than the slope of the budgetline

� If the consumer could give up more frozenyogurt for ice cream, he would do so

� However, there is no more frozen yogurt to giveup

� Opposite is true if corner solution was at point A



�When a corner solution arises, theconsumer’s MRS does not necessarilyequal the price ratio

� In this instance it can be said that:

YogurtFrozen

IceCream

P

PMRS ≥



� If the MRS is, in fact, significantly greaterthan the price ratio, then a smalldecrease in the price of frozen yogurt willnot alter the consumer’s market basket

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Budget Constraints - Otaru University of Commerceyamamoto/files/May_2.pdf©2005 Pearson Education, Inc. Chapter 3 1 Budget Constraints The Budget Line Indicates all combinations of