# HW0_answers - Jura Liaukonyte Econ 419 Spring 2007 Math...

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Jura Liaukonyte Econ 419 S pring 200 7 Math Review Questions (this is not for grades) 1. Find the derivate of the following cost functions with respect to q. a) 3 (12 ) q c q = 23 2 ) 3 ( 1) ) dc q q q dq q −− = b) 3 ln ) cq q =− 1 ln )3 ( ) dc qq q q dq +− c) q ce = q dc e dq = 2. Suppose that y is a function of x 1 and x 2 , find the values of x 1 and x 2 the maximize the following function: y=-(x 1 -1) 2 –(x 2 -2) 2 + 10 It will be easier if you rewrite the function as: 22 11 yx x x x + + + 5 now we need to maximize with with respect to x1 and x2. You need to use partial derivates. 1 1 2 2 1) 2 2 0 (we set it to zero because want to find max) y 2) 2 4 0 x y x x x + = You now gave two equations and two unknowns. Solving equation 1 and 2 we find the values that maximize this function are : * 1 x =1 * 2 x =2 (How do we know that this is max not min?)

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3. Suppose a firm’s total revenues depend on the amount produced (q) according to the function: R=70q-q 2 Total costs also depends on q: C=q 2 +30q+100 a) What level of output should the firm produce in order to maximize profits
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HW0_answers - Jura Liaukonyte Econ 419 Spring 2007 Math...

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