Microeconomics precourse – Part 2 Academic Year Course Presentation This course aims to prepare students for the Microeconomics course of the MSc in BA. It provides the essential background in microeconomics 1 PAOLO PAESANI Office: Room B6, 3RD floor, Building B Telephone: Office hours: to be agreed

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 2

Micro m = p 1 x 1 + p 2 x 2 x 2 = (m/p 2 ) - (p 1 /p 2 ) x 1 Data (nominal) m = money to be spent p 1 = unit price of good 1 p 2 = unit price of good 2 (p 1 /p 2 ) = relative price 3 Varian (2010) BUDGET CONSTRAINT

Micro 4 Varian (2010) BUDGET CONSTRAINT

Micro 5 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 )

Micro 6 Varian (2010) PREFERENCES We can represent preferences by means of indifference curves Axioms defining rational preferences

Micro 7 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 )

Micro 8 Varian (2010) PREFERENCES

Micro 9 UTILITY FUNCTION

Micro 10 THE COBB-DOUGLAS UTILITY FUNCTION Total utility : U(x 1, x 2 )=(x 1 ) a (x 2 ) b a,b > 0 Total utility the individual derives from consuming a given bundle Marginal utility of good 1: MUX 1 (x 1, x 2 )= ∂U/∂x 1 = a(x 1 ) a-1 (x 2 ) 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: MUX 1 (x 1, x 2 )=b(x 1 ) a (x 2 ) b-1 Additional utility the individual derives from marginally increasing his consumption of good 2 for a given quantity of good 1

Micro 11 MARGINAL RATE OF SUBSTITUTION MRS = dX 2 / dX 1 = MUX 1 /MUX 2 = a(x 1 ) a-1 (x 2 ) b /b(x 1 ) a (x 2 ) b-1 = a(x 2 )/b(x 1 ) The marginal rate of substitution measures the slope of the indifference curve in absolute value

Mic ro 12 THE CONSUMER BEHAVIOUR A D E

Micro 13 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

Micro 14 THE CONSUMER BEHAVIOUR : MATHEMATICAL SOLUTION 1.a(x 2 )/b(x 1 ) = (p 1 /p 2 ) 2.x 2 = (m/p 2 ) - (p 1 /p 2 ) x 1 Solving the system composed by Equations 1 and 2 we obtain the consumer’s demand functions for good 1 and good 2 3. x 1 = (a/a + b)(m/p 1 ) 4. x 2 = (b/a + b)(m/p 2 )

Micro 15 Varian (2010) CONSUMER’S BEHAVIOUR SPECIAL CASES

Micro 16 RELATIONSHI P BETWEEN INCOME AND INDIVIDUAL DEMAND Varian (2010)

Micro 17 RELATIONSHI P BETWEEN PRICE AND INDIVIDUAL DEMAND Varian (2010)

Micro 18 EFFECTS OF PRICE CHANGES INCOME AND SUBSTITUTIONS EFFECTS

Micro 19 REFERENCE Varian H. (1992) Microeconomic Analysis, 3rd edition, W. W. Norton & Company Varian H. (2010) Intermediate Microeconomics, 8° edition, W. W. Norton & Company