Transcript economia.uniroma2.it

Microeconomics precourse – Part 2
Academic Year 2013-2014
Course Presentation
This course aims to prepare students for the Microeconomics
course of the MSc in BA. It provides the essential background in
microeconomics
PAOLO PAESANI
Office: Room B6, 3RD floor, Building B
Telephone: 06-72595701
E-mail: [email protected]
Office hours: to be agreed
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CONSUMER THEORY
•
Rational agents try to get as much as they can out of
resources for a given objective function and a set of
constraints.
•
Rational consumers try to get as much as much satisfaction
as they can out of their money spending it at market prices.
•
Main elements of consumer theory:
• Budget constraint
• Preferences and utility function
• Optimal choice
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BUDGET CONSTRAINT
m = p1x1 + p2x2
x2 = (m/p2) - (p1/p2) x1
Data (nominal)
m = money to be spent
p1 = unit price of good 1
p2 = unit price of good 2
(p1/p2) = relative price
Varian (2010)
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BUDGET CONSTRAINT
Varian (2010)
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BUDGET CONSTRAINT
Points above the budget constraint indicate unaffordable bundles
Points below the budget constraint indicate bundles which the consumer
can afford to buy saving some money (but saving in a one period model is
irrational)
If income and prices change by the same factor the budget line does not
move (homogeneity of degree 0)
The shape of the budget constraint is affected by rationing, taxes and
subsidies (on this see Varian 2010, pp. 26-31)
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PREFERENCES
Axioms defining rational preferences
We can represent preferences by
means of indifference curves
Varian (2010)
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PREFERENCES
Points above the indifferent curve going through bundle A indicate
bundles which the individual weakly prefers to bundle A itself
Points below the indifferent curve going through bundle A indicate
bundles which the individual considers weakly inferior to bundle A itself
Points along the indifferent curve going through bundle A indicate
bundles which the individual finds equivalent to bundle A itself
Indifference curve representing rational preferences cannot intersect (on
this see Varian 2010, pp. 26-31)
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PREFERENCES
Varian (2010)
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UTILITY FUNCTION
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THE COBB-DOUGLAS UTILITY FUNCTION
Total utility : U(x1, x2)=(x1)a(x2)b a,b > 0
Total utility the individual derives from consuming a given bundle
Marginal utility of good 1: MUX1(x1, x2)= ∂U/∂x1= a(x1)a-1(x2)b
Additional utility the individual derives from marginally increasing his
consumption of good 1 for a given quantity of good 2
Marginal utility of good 2: MUX1(x1, x2)=b(x1)a(x2)b-1
Additional utility the individual derives from marginally increasing his
consumption of good 2 for a given quantity of good 1
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MARGINAL RATE OF SUBSTITUTION
MRS
=
dX2/ dX1
=
MUX1/MUX2
=
a(x1)a-1(x2)b/b(x1)a(x2)b-1
=
a(x2)/b(x1)
The marginal rate of substitution
measures the slope of the
indifference curve in absolute value
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THE CONSUMER BEHAVIOUR
E
D
A
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THE CONSUMER’S BEHAVIOUR : MATHEMATICAL SOLUTION
The optimal consumption bundle is characterised by two conditions
Tangency condition between the budget line and the indifference curves. The
slope of the budget line (which is equal to the relative price of the two goods
p1/p2) is equal to the slope of the indifference curve (which is equal to the
marginal rate of substitution).
Budget condition: the optimal bundle belongs to the budget line (in a one
period enviroment rational consumers spend all their money)
Translating these two condition in mathematical terms we obtain
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THE CONSUMER BEHAVIOUR : MATHEMATICAL SOLUTION
1. a(x2)/b(x1) = (p1/p2)
2. x2 = (m/p2) - (p1/p2) x1
Solving the system composed by Equations 1 and 2 we obtain the
consumer’s demand functions for good 1 and good 2
3. x1 = (a/a + b)(m/p1)
4. x2 = (b/a + b)(m/p2)
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CONSUMER’S BEHAVIOUR SPECIAL CASES
Varian (2010)
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RELATIONSHI P BETWEEN INCOME AND INDIVIDUAL DEMAND
Varian (2010)
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RELATIONSHI P BETWEEN PRICE AND INDIVIDUAL DEMAND
Varian (2010)
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REFERENCE
Varian H. (1992) Microeconomic Analysis, 3rd edition,
W. W. Norton & Company
Varian H. (2010) Intermediate Microeconomics, 8°
edition, W. W. Norton & Company
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