Lecture7

# Lecture7 - Lecture 7 Hicks Decomposition example Market...

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Lecture 7 Hicks Decomposition example Market Demand Price elasticity of demand Income elasticity of demand Consumer surplus

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Hicks Decomposition: Example U(X,Y) = XY p x = p y = 2 Income = I = 4 MUx = Y; MUy = X Two equations for equilibrium: pxX + pyY = 4 => 2X + 2Y = 4 °± ² °± ³ = ´ µ ´ · ¸ = 2 2 = 1 ⇒ ¹ = º = 1 => U(X,Y) = 1 Let the price of X decline to 1 Two equations for equilibrium: pxX + pyY = 4 => X + 2Y = 4 °± ² °± ³ = ´ µ ´ · ¸ = 1 2 ⇒ ¹ = »º Substituting: 2Y + 2Y = 4 => Y = 1 and X = 2Y = 2 1 2 1 X Y A B
Hicks Decomposition, cont. Find tangency of first indifference curve and a line with the slope of the second budget constraint: XY = 1 and a line with slope ½ Slope of tangent = (-1)MRS. Conditions: MRS = ½ = Y/X => 2Y = X XY = 1 => 2YY = 2Y 2 = 1 => Y 2 = ½ => Y = √ 1/2 X = 2√ 1/2 ( = point C on the graph) Substitution Effect: 2√ 1/2 – 1 Income Effect: 2 - 2√ 1/2 2 1 X Y A B C

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## This note was uploaded on 01/17/2012 for the course ECON 100A taught by Professor Safarzadeh during the Fall '09 term at UC Irvine.

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Lecture7 - Lecture 7 Hicks Decomposition example Market...

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