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Mdtrm1_sampl_problm

# Mdtrm1_sampl_problm - Ch 5 5.7 5.10 5.15 5.17 Ans 5.7 a...

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Ch 5: 5.7, 5.10, 5.15, 5.17 Ans: 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. 5.10 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, 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

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Mdtrm1_sampl_problm - Ch 5 5.7 5.10 5.15 5.17 Ans 5.7 a...

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