ps 2 solutoins

# ps 2 solutoins - Intermediate Microeconomics Summer 2007...

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1 Intermediate Microeconomics Monika Thomas Summer 2007 Solutions: Problem Set 2 5.7 a) Denoting the level of income by I , the budget constraint implies that I y p x p y x = + and the tangency condition is y x p p x = 2 1 , which means that 2 2 4 x y p p x = . The demand for x does not depend on the level of income. b) From the budget constraint, the demand curve for y is, x y y y x p p p I p x p I y 4 - = - = . You can see that the demand for y increases with an increase in the level of income, indicating that y is a normal good. Moreover, when the price of x goes up, the demand for y increases as well.

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2 5.8 a) A B C Substitution Effect Income Effect X Y b) A B C Substitution Effect X Y Income Effect = 0
3 c) A B C Substitution Effect X Y Income Effect d) A B C Substitution Effect X Y Income Effect

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4 5.16 a) Using the tangency condition, 4 = x y , and the budget constraint, 120 4 = + y x , Lou’s initial optimum is the basket ( x , y ) = (15, 60) with a utility of 900. b) First we need the decomposition basket. This would satisfy the new tangency condition, 3 = x y and would give him as much utility as before, i.e. 900 = xy . This gives ) 3 30 , 3 10 ( ) , ( = y x or approximately (17.3,51.9). Now we need the final basket, which satisfies the same tangency condition as the decomposition basket and also the new budget constraint: . 120 3 = + y x Together, these conditions imply that ( x , y ) = (20, 60). The substitution effect is therefore 17.3 – 15 = 2.3, and the income effect is 20 – 17.3 = 2.7. c) The compensating variation is the amount of income Lou would be willing to give up after the price change to maintain the level of utility he had before the price change. This equals the difference between the
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ps 2 solutoins - Intermediate Microeconomics Summer 2007...

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