Problem Set 3 - Solutions

Problem Set 3 - Solutions - Ginger reaches exactly the same...

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ECON – 301 Problem Set 3 – Solutions 1) 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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ECON – 301 2) a) The budget constraint is 240 2 8 y x and the tangency condition is 4 2 8 2 x y . Solving, the optimal bundle is ( x , y )=(20, 40) with a utility of 20 2 (40)=16,000. b) Now p y =8. We need to calculate p x such that, with the new prices,
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Unformatted text preview: Ginger reaches exactly the same indifference curve as before. The new optimal bundle (x,y) must be such that: 16000 and , 240 8 2 y x y x p x . The tangency condition now implies that 8 2 x p x y that is, . 16 y x p x Substituting this into the budget constraint we find that y =10. Using the condition 16000 2 y x , we find that x = 40. Finally, substituting the values of x and y back into the budget constraint, we can see that 240 ) 10 ( 8 40 x p , or p x =4. Therefore, if the price of y were to increase to $8, Ginger would need the price of x to decrease to $4 in order to be exactly as well off as before....
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This note was uploaded on 05/11/2011 for the course ECON 301 taught by Professor Sheng during the Spring '11 term at ITT Tech Pittsburgh.

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Problem Set 3 - Solutions - Ginger reaches exactly the same...

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