PS4AK_winter2010

# PS4AK_winter2010 - Problem Set 4: Answer Key 1. (a) In...

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Problem Set 4: Answer Key 1. (a) In order to derive the consumer’s demand curve, we can solve the utility maximizing problem of the consumer i.e. Thus, we can construct the Lagrangian: Now, to solve for the demand functions of goods A and goods B, we need to take the partial derivative of the expression above with respect to A , B and the multiplier: 1. 2. 3. Dividing equation 1 by equation 2, we get: Finally, using the above relation in equation 3, we get: . This implies that the demand for good B is (b) Recall that when we are deriving the market demand curve, we sum over quantities rather than prices. In this case, we have that 1000 consumers have the demand function derived above. So, in this case, we imagine prices to be fixed and sum over our set of consumers. For a given price , individual demand for good B is . So, the cumulative demand for 1000 consumers will be . Now, we also have that there are 1000 consumers with an income of \$2400. What will be the individual demand in this case? Note that the only thing changing here is that the income has doubled. Given the same utility and price levels,

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## This note was uploaded on 03/11/2010 for the course ECN ECN100 taught by Professor Stevens during the Winter '09 term at UC Davis.

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PS4AK_winter2010 - Problem Set 4: Answer Key 1. (a) In...

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