L5Choices - Introductionto Microeconomics Lecture5...

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1 Introduction to Microeconomics Lecture 5 Choices in Action Ian Crawford Review z Consumers choose the set of goods they most prefer, out of the set of goods they can afford. z We use utility functions/indifference curves to give formal content to “most prefer” z We use budget sets/constraints to give formal content to “can afford”. Review z In due course this becomes a constrained maximisation problem which you can solve mathematically “Maximise utility, subject to the budget constraint.” z So far you’ve learned how to solve the problem graphically for two goods ... ( ) 1 2 1 2 1 1 2 2 , ,..., max , ,..., subject to ... n n n n x x x u x x x p x p x p x m + + + Review x 2 Optimal choice ( ) * 2 * 1 , x x 0 x 1 * 1 x * 2 x Sub optimal choice #2 Sub optimal choice #1 Review z Given an indifference curve map you can change prices and income and work out the demands each time: { } { } 1 2 1 2 , , , p p m x x z Keep this up and you’ll map out the Marshallian Demand Functions { } { } { } { } 1 2 1 2 1 2 1 2 , , , ˆ ˆ ˆ ˆ ˆ , , , p p m x x p p m x x % % % % % ( ) ( ) 1 1 2 2 1 2 , , , , x p p m x p p m Outline z Properties of Marshallian Demands z Measuring changes elasticities z Income Changes z Price Changes z Decomposing price changes z Substitution and income effects z The Slutsky Equation z Modelling the labour supply (leisure demand) decision the Working Tax Credit [we may not get this far today]
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2 Measuring the Effects of Change – “Elasticities” z y depends upon x: z Change x a bit: Look at the change in y: ( ) y f x = ( ) x x x Δ = ( ) y y y Δ z z We could compare and to measure responsiveness, but the answer would depend on the units. z Economists use “elasticities” instead / Proportional change in The elasticity of : / Proportional change in yx y y y x y x x x ε Δ = = Δ = y Δ x Δ Measuring the Effects of Change – “Elasticities” Take a Marshallian demand function: 1 1 1 1 1 1 / The own price elasticity of demand : / x p x x x p p p p x ε Δ Δ = = Δ Δ ( ) 1 1 2 , , x p p m 1 2 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 / The cross price elasticity of demand : / / The income elasticity of demand : / x p x m x x x p p p p x x x x m m m m x ε ε Δ Δ = = Δ Δ Δ Δ = = Δ Δ x 2 Measuring the Effects of Change – Income Elasticities 1 1 1 / 0 0 / 0 / 0 x m x x m m x x ε Δ > = = > Δ > Δ > 0 x 1 1 x Δ 2 x Δ 2 2 2 0 / 0 x m m m ε = = > Δ > Both are “ Normal goods x 2 Measuring the Effects of Change – Income Elasticities 1 1 1 / 0 0 / 0 / 0 x m x x m m x x ε Δ < = = < Δ > Δ > x 1 0 1 x Δ 2 x Δ 2 2 2 0 / 0 x m m m ε = = > Δ > is a normal good Is an “Inferior Good” x 1 x 2 Measuring the Effects of Change – Income Elasticities “Necessities” “Luxuries” 0 1 i x m ε < < 1 i x m ε < 0 Inferior Goods 1 Normal Goods Income Elasticities 0 i x m ε < 0 i x m ε > x 2 Measuring the Effects of Change – Price Elasticities The price of good 1 falls. Demand for good 1 rises x 1 0 1 x Δ 1 1 1 1 1 1 / 0 0 / 0 x p x x p p ε Δ > = = < Δ < Good 1 is an “Ordinary Good”
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