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aps2 - Intermediate Microeconomics Wissink BRIEF ANSWERS TO...

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Intermediate Microeconomics - Wissink BRIEF ANSWERS TO PROBLEM SET #2 1. The demand systems would be as follows: For u=ax+by you get either one corner or the other depending on how a/b compares to the price ratio. So, x*=I/p x and y*=0 when a/b>p x /p y and y*=I/p y and x*=0 otherwise (Note that when a/b = p x /p y I have opted to consume only y. Really, any combination of x and y would work in that knife edge case.) For u=min{ax, by} you have to recognize that you always want ax=by. Therefore x=(by)/a. Now plug that into the budget line and solve for y and you get: p x x+p y y=I where x=(by)/a. You eventually get: y*=(aI)/(bp x +ap y ) and x*=(bI)/(bp x +ap y ). 2. The Price Consumption Curve (PCC) (or price offer curve)for a change in the price of x looks as follows: y x PCC u=xy p /p x y = 1 PCC y x u=x+y y x PCC u=min{x,y}
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2 y x u=xy E E E 0 1 H 3. The Income Consumption Curves (ICC) - or income offer curves - look as follows: ICC u=xy y x ICC u=min{x,y} y x 4. The income and substitution effects for an increase
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