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Microeconomics precourse – Part 2Academic Year 2013-2014

Course PresentationThis 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: paolo.paesani@uniroma2.itOffice 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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m = p1x1 + p2x2 x2 = (m/p2) - (p1/p2) x1

Data (nominal)m = money to be spentp1 = unit price of good 1p2 = unit price of good 2

(p1/p2) = relative price

Varian (2010)

BUDGET CONSTRAINT

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Varian (2010)

BUDGET CONSTRAINT

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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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Varian (2010)

PREFERENCES

We can represent preferences by means of indifference curves

Axioms defining rational preferences

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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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Varian (2010)

PREFERENCES

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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 > 0Total 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

A

D

E

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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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Varian (2010)

CONSUMER’S BEHAVIOUR SPECIAL CASES

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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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EFFECTS OF PRICE CHANGES INCOME AND SUBSTITUTIONS EFFECTS

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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