Solutions Homework Assignment 1 411

Solutions Homework Assignment 1 411 - Solutions Homework...

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Unformatted text preview: Solutions Homework Assignment 1 2.1 2 2 ( , ) 4 3 = + U x y x y a. 8 6 ! ! ! ! U U = x , = y x y b. 8, 12 c. 8 6 ! ! = ! ! U U dU dx + dy = x dx + y dy x y d. for 0 8 6 = + = dy dU x dx y dy dx 8 4 6 3 ! ! dy x x = = dx y y e. 1, 2 4 1 3 4 16 = = = ! + ! = x y U f. 4(1) 2 / 3 3(2) ! = = ! dy dx g. U = 16 contour line is an ellipse centered at the origin. With equation 2 2 4 3 16 + = x y , slope of the line at ( x, y ) is 4 3 = ! dy x dx y . 2.2 a. Profits are given by 2 2 40 100 ! = " = " + " R C q q * 4 40 10 ! = " + = d q q dq 2 * 2(10 40(10) 100 100 ) ! = " + " = b. 2 2 4 ! = " d dq so profits are maximized c. 70 2 = = ! dR MR q dq 2 30 = = + dC mC q dq so q * = 10 obeys MR = MC = 50. 2.3 Substitution: 2 1 so = ! = = ! y x f xy x x 1 ¡ ! = " = ! f x x 0.5 0.5, 0.25 x = , y = f = Note: ¡ !! = " < f . This is a local and global maximum. Lagrangian Method: £ (1 ) !...
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This note was uploaded on 11/22/2010 for the course ECON 411 taught by Professor Ann during the Fall '10 term at Oregon.

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Solutions Homework Assignment 1 411 - Solutions Homework...

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