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

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

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Unformatted text preview: 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: < < ≥ < < ≥ ≥ ≥ + = and if and if and if and 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 Economics 3070-008 Fall 2007 + + + + + + ≤ + + + +- + + + + ≤ + +- + + ≤ + + ≤ + + +- = 2 1 2 1 2 2 1 1 2 1 2 1 02 2 5 and 005 2 5 if 02 2 5 and 005 2 5 if 02 . 2 . 5 02 2 5 and 005 2 5 if 01 . 4 . 2 10 02 2 5 and 005 2 5 if 02 . 01 . 6 . 3 15 I . P . P I . P . P I .....
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3070_PSet-2_Solutions%20(joe%20edit%20ps1)[1] - Economics...

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