Consumer Theory in Intermediate Microeconomics: Budget Constraints and Price Changes, Exercises of Microeconomics

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Intermediate Microeconomics

ECO 220 / 221

CONSUMER THEORYCONSUMER

THEORY

We will look at1.^ Scarcity: income and prices2.^ Tastes 3 Combine scarcity and tastes3.^ Combine scarcity and tastes(i) Individual demand( ) (ii) Market demand

Budget Set and Constraint forTwo Productsx 2

Budget constraint isp x^ + p x

=^ m m^ /p^2

p^ x+ p^ x^1 1

=^ m 2 x m /p 11

Budget Set and Constraint forTwo Productsx 2 m /p 2

Budget constraint isp x^ + p x

=^ m p^ x+ p^ x^1 1

=^ m 2 x m /p 11

• Budget Set and Constraint forTwo Productsx 2 m /p
  • Not affordableJust affordablex m /p

Budget Set and Constraint forTwo Productsx 2 m /p 2

Not affordableAff^ d bl^ (i

ti^ l) Just affordableAffordable (irrational)x

1 m^ /p^1

Budget Set and Constraint forTwo Productsx 2 p

x+ p^ x 1 1 2 2

=^ m Re-arranging (as before) m^ /p^2

g^ g (^

x= - (p^ /p^2

)x+^ m /p 2 1

2 so slope is – (p

/p^ ) 1 2 so slope is

(p^ /p^ )^1 BudgetSet

x^1 m^ /p^1 Set

SCARITYBudget ConstraintBudget Constraint

M/pX 2 2^ p

X+pX= M 1122 2

p^ X^ 1X1+p^22

M

SlopeSlope^  X^ /^  X^ = - (p^2

/p^ ) 1 2 M/p^1 Budget Set

X^1

The slope of the income constraint represents society’s willingness top^

p^ y

g

trade; to increase consumption of product 1 by 1 unit, an individualmust decrease consumption of product 2 by P

/Punits^12.

“ OPPPORTUNITY COST

”

INCOME CHANGESINCOME

CHANGES

^ No original choice is lost and newchoices are added when incomeincreases, so higher income willmake a consumer better off. ^ Trade off between products [– (p

/p^ )] 1 2

remains unchangedremains unchanged.  An income decrease will make the

ff consumer worse off.

How do the budget set and budgett^ i t

h^

d constraint change as

p^ decreases^1 (^0) (from p 1 1 to^ p^ )?^1 x^2

(from^ p^1

to^ p )?^1 (^2) m/p^2

(^101 0) P <P^ P<P (^11) Ratio of P/P^1 changes Slope changes Originalbudget setg

x^1 (^0) m/p 1

(^1) m/p 1

How do the budget set and budgett^ i t

h^

d constraint change as

p^ decreases^1 (^0) from p 1 (^1) to p? 1 x^2

from^ p^1

to^ p?^1 (^2) m/p^2 New affordable choices^00 p^ /p-p^ /p^1

(^2) Originalbudget setg

x^1 (^0) m/p 1

(^1) m/p 1

How do the budget set and budgett^ i t

h^

d constraint change as

p^ decreases^1 (^0) from p 1 (^1) to p? x^2

from^ p^1

to^ p^? (^2) m/p^2 New affordable choices

Budget constrainti t^ l^

fl tt (^0) p /p^

pivots; slope flattensfrom -p

(^0) /pto 12 (^0) -p /p^12 Originalbudget set

(^1) -p/p 12 (^1) -p /p^12 g

x^1 (^0) m/p 1

(^1) m/p 1

PRICE CHANGES IIPRICE^ CHANGES II Cl i A d^ bli^

f^ ll^ i^

i Claim: A doubling of all prices isequivalent to halving income.PX+ PX^1 1 2

= M Let all prices change by a factor of t(e.g. t = 2)(tP)X+ (tP^1

)X= M 2 2 ^ PX+ P^1

X= M/t (i.e. equivalent to a 2 2 ^ PXP^1

XM/t (i.e. equivalent to a 2 2 parallel shift in the income constraint)(Relatuve prices remain unchanged.)(Relatuve prices remain unchanged.)

COMPOSITE

PRODUCT

COMPOSITE

PRODUCT n products?

PX+ PX^1 1 2

+^ + P

X= Mnn^ PX+ PX^1 1 2

• …….. + P

XMnn^ P X^ [P X^

P X^

P X ]^ M PX+ [PX^1 1 2

• PX+ …….. + P 3 3

X] = Mnn [PX+ PX^2 2

• …….. + P 3

X] representsnn income spent on all products other thanp^

p product 1, that is, income spent on acomposite product.p^

p