micro_hw3_solution

micro_hw3_solution - Fall 2007 73-150 Microeconomics...

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1 Fall 2007 73-150 Microeconomics Problem Set #3 Solution Keys Exercise The quantity demanded for a Giffen good will increase when there is a price increase. In other words, the quantity demanded for a Giffen good will decrease when price drops (price , quantity ). Since the substitution effect of a price decrease will always increase the quantity demanded (p x , x ), the Giffen good must be a good whose income effect overcomes the substitution effect. A Giffen good is a strongly inferior good whose quantity demanded drops when income is higher: income , quantity . Assume x is a Giffen good. If the price of x drops, because we know the net effect and the substitution effect of a price drop on quantities for a Giffen good, so we can figure out the income effect on x. Substitution effect: p x , x Income effect: p x , x ? Net effect: x Because of the resultant drop in x, the income effect of x must be a decrease in quantity. Income effect of a price drop in x, will reduce the quantity demanded for x. Substitution Effect Income Effect x y slope= y x p p ' slope= y x p p C A B p’ x < p x slope= y x p p '
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Graphing: We know that p’ x < p x Æ y x y x p p p p < ' , so the new budget constraint is flatter than the old one. From point A to point B is the substitution effect because it is on the same indifference curves, and from B to point C is the income effect because the two budget lines tangent to each point have the same slopes. 1) a) U(x, y) = x 2 y 5 Maximize: U(x, y) = x 2 y 5 subject to: p x x+p y y I , x 0, y 0 M R S = y x p p at the optimal bundle. M R S = y x MU MU = x y y x xy 5 2 5 2 4 2 5 = x y 5 2 = y x p p Î y= y x p p 2 5 x I= p x x+p y y = p x x + p y 2 5 y x p x p = p x x (1+ ) 2 5 = 2 7 p x x I= 2 7 p x x x= x p I 7 2 Î we know that y= y x p p 2 5 x , so y= y x p p 2 5 x p I 7 2 = y p I 7 5 Demand functions: x* = x p I 7 2 y* = y p I 7 5 b) Perfect complements: U(x, y) = min{2x,5y} Budget constraint is still: p x x+p y y I The set of bundles that are tangent to the budget constraint all go through the line 2x=5y Î y= 5 2 x . p
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micro_hw3_solution - Fall 2007 73-150 Microeconomics...

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