3070_PSet-2_Solutions%20(joe%20edit%20ps1)[1]

3070_PSet-2_Solutions%20(joe%20edit%20ps1)[1] - Economics...

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Economics 3070-008 Fall 2007 Problem Set 1 Solutions 1. Suppose there are only two goods ( X  and  Y ) and only two individuals (numbered  1 and 2) in an economy.  Let  P X  be the price of good  X  and  P Y  be the price of  good  Y .  And finally, let  I 1  represent the income of individual 1 and  I 2  the income  of individual 2. Suppose the quantity of good  X  demanded by individual 1 is given by X 1  = 10 – 2  P X  + 0.01  I 1  + 0.4  P Y  , and the quantity of  X  demanded by individual 2 is X 2  = 5 –  P X  + 0.02  I 2  + 0.2  P Y  . a. What is the market demand function for total  X  (=  X 1  +  X 2 ) as a function of  P X I 1 I 2 , and  P Y ? The market demand function is, generally, the sum of the two individual demand  functions.  The exception occurs when the quantity demanded by a particular  individual is negative:  in this case, you don’t want to add a negative quantity to  the total quantity demanded (you want to just add zero).  This gives us the  following framework for constructing the market demand function: < < < < + = 0   and   0   if 0 0   and   0   if 0   and   0   if 0   and   0   if 2 1 2 1 2 2 1 1 2 1 2 1 X X X X X X X X X X X X X After plugging in the for  X 1  and  X 2 , we obtain
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Economics 3070-008 Fall 2007 + + + + + + + + + + - + + + + + + - + + + + + + + - = 2 1 2 1 2 2 1 1 2 1 2 1 02 0 2 0 5   and   005 0 2 0 5   if 0 02 0 2 0 5   and   005 0 2 0 5   if 02 . 0 2 . 0 5 02 0 2 0 5   and   005 0 2 0 5   if 01 . 0 4 . 0 2 10 02 0 2 0 5   and   005 0 2 0 5   if 02 . 0 01 . 0 6 . 0 3 15 I . P . P I . P . P I . P . P I . P . P I P P I . P . P I . P . P I P P I . P . P I . P . P I I P P X Y X Y X Y X Y X Y X Y X Y X Y X Y X Y X Y X b.
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