lecture 3: demand neoclassical theory of...
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Lecture 3: DemandNeoclassical Theory of Consumption
Economics II: Microeconomics
V�E Praha
October 2009
Micro (V�E) Consumption theory 10/09 1 / 28
Economics II: Microeconomics
Consumers:
People.Households.Applications.
Firms:
Internal Organisation.Industrial Organisation.
Equilibrium:
Holds.Does not hold.
Micro (V�E) Consumption theory 10/09 2 / 28
Microeconomics
Consumers:
People.� NowHouseholds.Applications.
Firms:
Internal Organisation.Industrial Organisation.
Equilibrium:
Holds.Does not hold.
Micro (V�E) Consumption theory 10/09 3 / 28
Neoclassical theory of consumptionBasics
PEOPLE CHOOSE THE BEST THINGS THEY CAN AFFORD.
PEOPLE CHOOSE THE MOST PREFERRED BUNDLE THEY CAN AFFORD.
Consumers CHOOSE THE MOST PREFERRED BUNDLE THEY CAN AFFORD.
De�nitionA consumer is an economic agent who makes a decision on consumption.
Micro (V�E) Consumption theory 10/09 4 / 28
Neoclassical theory of consumptionBasics: A¤ordable Bundles
FactThe slope of BC = - pzpB .
De�nitionBudget constraint:The bundles of goods thatcan be bought if the entirebudget is spent on thosegoods at given prices.
ExampleBudget constraint:p1x1 + p2x2 = m.
x2 =mp2|{z}
intercept
�p1p2|{z}
slope
� x1
Micro (V�E) Consumption theory 10/09 5 / 28
Budget ConstraintShifts in prices and income
Micro (V�E) Consumption theory 10/09 6 / 28
Neoclassical theory of consumptionBasics
CONSUMERS CHOOSE THE MOST PREFERRED BUNDLE FROM THEIRBUDGET SET.
Micro (V�E) Consumption theory 10/09 7 / 28
Neoclassical theory of consumptionConsumer�s choice
FactConsumers�choice is a comboof their preferences andbudget.
Micro (V�E) Consumption theory 10/09 8 / 28
Neoclassical theory of consumptionConsumer�s choice
FactConsumers�choice is a comboof their preferences andbudget.
LemmaConsumer chooses the bundlewhere the indiference curve istangent to the budget line.
Micro (V�E) Consumption theory 10/09 9 / 28
Neoclassical theory of consumptionConsumer�s choice
Micro (V�E) Consumption theory 10/09 10 / 28
Neoclassical theory of consumptionConsumer optimisation problem: Calculus approach
Problemmaxx1,x2
U (x1, x2) ,.
s.t. p1x1 + p2x2 = m
Problem (Lagrange function)
maxx1,x2,λ
L = U (x1, x2) + λ (m� p1x1 � p2x2)
Micro (V�E) Consumption theory 10/09 11 / 28
Neoclassical theory of consumptionConsumer optimisation problem: Calculus approach
Problemmaxx1,x2,λ
L = U (x1, x2) + λ (m� p1x1 � p2x2)
SolutionFirst order conditions:
∂L∂x1
= 0 :∂U (x1, x2)
∂x1� λp1 = 0 (1)
∂L∂x2
= 0 :∂U (x1, x2)
∂x2� λp2 = 0 (2)
∂L∂λ
= 0 : m� p1x1 � p2x2 = 0 (3)
Micro (V�E) Consumption theory 10/09 12 / 28
Neoclassical theory of consumptionConsumer optimisation problem (Cont�d)
Problem
SolutionFrom (1) and (2): �
MUx1MUx2
=
� ∂U (x1,x2)∂x1
∂U (x1,x2)∂x2
=p1p2
(4)
Equations (3) and (4) give the solution: x�1 (p1, p2,m) and x�2 (p1, p2,m)
De�nitionThe pair (x�1 , x
�2 ) is the optimal choice of the consumer.
De�nitionDemand function: x = x (p1, p2,m)
Micro (V�E) Consumption theory 10/09 13 / 28
Utility function and indi¤erence curves
The indi¤erence curve is the utility function on a �xed level.
Micro (V�E) Consumption theory 10/09 14 / 28
Consumer Optimisation Problem
Full derivative of the utilityfunction U (x1, x2) :
dU =∂U∂x1
� dx1 +∂U∂x2
� dx2(5)
FactThe indi¤erence curve is theutility function on a �xed level.
So (5) can be rewritten as:
∂U (x1,x2)∂x1
∂U (x1,x2)∂x2
= �dx2dx1
(6)
CorollaryFrom (4) and (6) we have:
MRS =p1p2
(7)
FactThe internal rate of change isequal to the external rate ofchange.
Micro (V�E) Consumption theory 10/09 15 / 28
Consumer Optimisation ProblemNecessary condition
MRS =p1p2
internal RCh = external RCh
slope IC = slope BC
bene�t of consumingx1 as opposed to x2
=opportunity cost ofx1 in terms of x2
Micro (V�E) Consumption theory 10/09 16 / 28
Next lecture
Further studies in Neoclassical Theory!
Thank you!
Micro (V�E) Consumption theory 10/09 17 / 28
Neoclassical theory of consumptionDemand function
De�nitionDemand:The quantity demanded ateach possible price.
Demand function:
x1 = x1 (p1, p̄2, m̄)
Comparative statics
Shifts in m.Shifts in p1.Shifts in p2.
Micro (V�E) Consumption theory 10/09 18 / 28
Neoclassical theory of consumptionDemand function
De�nitionDemand:The quantity demanded ateach possible price.
Demand function:
x1 = x1 (p1, p̄2, m̄)
Comparative statics
Shifts in m.Shifts in p1.Shifts in p2.
Micro (V�E) Consumption theory 10/09 18 / 28
Neoclassical theory of consumptionDemand function
De�nitionDemand:The quantity demanded ateach possible price.
Demand function:
x1 = x1 (p1, p̄2, m̄)
Comparative statics
Shifts in m.
Shifts in p1.Shifts in p2.
Micro (V�E) Consumption theory 10/09 18 / 28
Neoclassical theory of consumptionDemand function
De�nitionDemand:The quantity demanded ateach possible price.
Demand function:
x1 = x1 (p1, p̄2, m̄)
Comparative statics
Shifts in m.Shifts in p1.
Shifts in p2.
Micro (V�E) Consumption theory 10/09 18 / 28
Neoclassical theory of consumptionDemand function
De�nitionDemand:The quantity demanded ateach possible price.
Demand function:
x1 = x1 (p1, p̄2, m̄)
Comparative statics
Shifts in m.Shifts in p1.Shifts in p2.
Micro (V�E) Consumption theory 10/09 18 / 28
Income expansion path and Engel curve
Income expansion path
Bundles demanded atdi¤erent income levelsIncome-consumptioncurveincome o¤er curve
Engel curve
x1 = x1 (p̄1, p̄2,m)
Demand as a functionof income only!
Q: Shape of IEP and EC
Micro (V�E) Consumption theory 10/09 19 / 28
Engel curve for perfect substitute
Micro (V�E) Consumption theory 10/09 20 / 28
Income elasticity & Engel curve
De�nitionThe income elasticity of demand (or income elasticity) is the precentagechange in the quantity demanded in response to a given percentagechange in income.
εM =%∆x1%∆m
=∆x1x1
∆mm
=
x 01�x1x1
m 0�mm
=∂x1∂m
� mx1
Note:
εM 6=∆x1∆m
Micro (V�E) Consumption theory 10/09 21 / 28
Income elacticity & Engel curve
Normal good : ε > 0
Inferior good: ε < 0
Quasilinear: ε = 0
Luxury goods: ε > 1
Necessities: ε < 1
Homothetic: ε = 1
Micro (V�E) Consumption theory 10/09 22 / 28
Income elacticity & Engel curve
Normal good : ε > 0
Inferior good: ε < 0
Quasilinear: ε = 0
Luxury goods: ε > 1
Necessities: ε < 1
Homothetic: ε = 1
Micro (V�E) Consumption theory 10/09 22 / 28
Income elacticity & Engel curve
Normal good : ε > 0
Inferior good: ε < 0
Quasilinear: ε = 0
Luxury goods: ε > 1
Necessities: ε < 1
Homothetic: ε = 1
Micro (V�E) Consumption theory 10/09 22 / 28
Income elacticity & Engel curve
Normal good : ε > 0
Inferior good: ε < 0
Quasilinear: ε = 0
Luxury goods: ε > 1
Necessities: ε < 1
Homothetic: ε = 1
Micro (V�E) Consumption theory 10/09 22 / 28
Income elacticity & Engel curve
Normal good : ε > 0
Inferior good: ε < 0
Quasilinear: ε = 0
Luxury goods: ε > 1
Necessities: ε < 1
Homothetic: ε = 1
Micro (V�E) Consumption theory 10/09 22 / 28
Income elacticity & Engel curve
Normal good : ε > 0
Inferior good: ε < 0
Quasilinear: ε = 0
Luxury goods: ε > 1
Necessities: ε < 1
Homothetic: ε = 1
Micro (V�E) Consumption theory 10/09 22 / 28
Neoclassical theory of consumptionDemand function (revisited)
Demand function:
x1 = x1 (p1, p̄2, m̄)
Comparative statics
Shifts in m.Shifts in p1.Shifts in p2.
Relative price as well asincome change!
Micro (V�E) Consumption theory 10/09 23 / 28
Income and Substitution E¤ect
De�nitionThe change in demand due to the change in the rate of exchange betweenthe two goods is called substitution e¤ect. (changed own price, other pricesand utility constant).
De�nitionThe change in demand due to the change in purchasing power is calledincome e¤ect. (prices are hold constant)
Micro (V�E) Consumption theory 10/09 24 / 28
Income and Substitution E¤ect
Substitution e¤ect is always negative due to the �well-behaved�indi¤erence curves!
What about the direction of the income e¤ect?
Micro (V�E) Consumption theory 10/09 25 / 28
Income and Substitution E¤ect
Substitution e¤ect is always negative due to the �well-behaved�indi¤erence curves!What about the direction of the income e¤ect?
Micro (V�E) Consumption theory 10/09 25 / 28
Income and Substitution E¤ect
Gi¤en goods (Inferior)
Micro (V�E) Consumption theory 10/09 26 / 28
Price and cross-price changes
Own price change
Ordinary goods:∂x1∂p1
< 0
Gi¤en goods:∂x1∂p1
> 0
Cross price change
substitute (not perfect)∂x1∂p2
> 0
complement (not perfect)∂x1∂p2
< 0
Micro (V�E) Consumption theory 10/09 27 / 28
Price and cross-price changes
Own price change
Ordinary goods:∂x1∂p1
< 0
Gi¤en goods:∂x1∂p1
> 0
Cross price change
substitute (not perfect)∂x1∂p2
> 0
complement (not perfect)∂x1∂p2
< 0
Micro (V�E) Consumption theory 10/09 27 / 28
Price and cross-price changes
Own price change
Ordinary goods:∂x1∂p1
< 0
Gi¤en goods:∂x1∂p1
> 0
Cross price change
substitute (not perfect)∂x1∂p2
> 0
complement (not perfect)∂x1∂p2
< 0
Micro (V�E) Consumption theory 10/09 27 / 28
Price and cross-price changes
Own price change
Ordinary goods:∂x1∂p1
< 0
Gi¤en goods:∂x1∂p1
> 0
Cross price change
substitute (not perfect)∂x1∂p2
> 0
complement (not perfect)∂x1∂p2
< 0
Micro (V�E) Consumption theory 10/09 27 / 28
Price and cross-price changes
Own price change
Ordinary goods:∂x1∂p1
< 0
Gi¤en goods:∂x1∂p1
> 0
Cross price change
substitute (not perfect)∂x1∂p2
> 0
complement (not perfect)∂x1∂p2
< 0
Micro (V�E) Consumption theory 10/09 27 / 28
Price and cross-price changes
Own price change
Ordinary goods:∂x1∂p1
< 0
Gi¤en goods:∂x1∂p1
> 0
Cross price change
substitute (not perfect)∂x1∂p2
> 0
complement (not perfect)∂x1∂p2
< 0
Micro (V�E) Consumption theory 10/09 27 / 28
Next lecture
Further applications!
Thank you!
Micro (V�E) Consumption theory 10/09 28 / 28