PS 2 Solution

# PS 2 Solution - Quantitative Microeconomics Answers to...

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Quantitative Microeconomics Answers to Problem Set #2 1) Slutsky equation: X / P X = ( h X / P X )- [( X/ M)*X] a) Lagrangian: L= XY 2 + λ (M- P Y Y- P X X ) i) First-order conditions (FOC): L/ Y = 2YX - λ P Y = 0 L/ X = Y 2 - λ P X = 0 L/ ∂λ =M- P Y Y- P X X =0 ii) Using the first and second FOC: [Y/2X ]=P X /P Y i.e. MRS =ratio of the prices This is equivalent to showing that the consumer is at his optimum when marginal benefits=marginal costs. [Y/2X] is simply the marginal benefit of food in terms of clothing since it is the slope of the indifference curve and is equivalent to the ratio of marginal utilities. Similarly, P X /P Y is simply the marginal cost of food in terms of clothing since it is simply the slope of the budget line. Rearranging this expression X=YP Y /2P X . iii) Substituting for X in the third FOC: M- P Y Y- P X [(Y P Y )/2P X ]=0 This condition is equivalent to saying that the constraint boundary condition principle is

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## This note was uploaded on 03/26/2008 for the course EC 16 taught by Professor Loury during the Fall '07 term at Tufts.

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PS 2 Solution - Quantitative Microeconomics Answers to...

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