Pset1Answers - EC115 Methods of Economic Analysis Problem...

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EC115 – Methods of Economic Analysis Problem Set 1 – Solutions 1. Find the solution to the following linear equations: (a) 0 8 4 = - x (b) 0 6 1 3 1 = - - x (c) x x 4 3 = + Check your answers graphically. Solution: (a) 2 = x Graphically: (b) 2 1 - = x -8 2 x Solution 8 4 - = x y y
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Graphically: (c) 1 = x . Note that the function could also be written as y = 3x – 3. We would then have an upward sloping graph with a y-intercept of -3. However, the solution of the linear equation is x = 1. 2. Consider the following implicit linear functions: (a) 0 20 2 10 = + - y x (b) 0 12 12 6 = - - - x y For each function, (i) Express y as a function of x 3 1 x y Solution y = 3x – 3 Solution -1/2 x y 6 1 3 1 - - = x y 3 3 + - = x y
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(ii) Plot the graph in (a) between x = -2 and x = 2 (iii)Plot the graph in (b) between x = 0 and x = 3. Solution: (i) (a) 10 5 + = x y ; (b) 2 2 - - = x y (ii) Graph of (a) between 2 - = x and 2 = x . First find at least two points to plot this linear function. If 2 - = x , then 0 = y , so the first point is (-2, 0). If 2 = x then 20 = y , so the second point is (2, 20). Graph of
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Pset1Answers - EC115 Methods of Economic Analysis Problem...

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