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answerstohomework1spring2008

answerstohomework1spring2008 - Economics 102 Spring 2008...

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Economics 102 Spring 2008 Answers to Homework 1 Question 1 (Simultaneous equations). Find the slopes of the following two linear functions: x y 7 6 + = , (1) x y 7 2 + - = . (2) (a). If these two equations were graphed in the same graph, would they intersect? Explain your answer. (b). Can you give a condition for two linear functions to have an intersection point? Answer 1 (Simultaneous equations). (a). ) , ( 1 1 y x and ) , ( 2 2 y x are any two points of function (1); 1 1 7 6 x y + = , 2 2 7 6 x y + = . Then 7 7 6 7 6 1 2 1 2 1 2 1 2 = - + - + = - - = x x x x x x y y x y . ) , ( 3 3 y x and ) , ( 4 4 y x are any two points of function (2); 3 3 7 2 x y + - = , 4 4 7 2 x y + - = . Then 7 ) 7 2 ( 7 2 3 4 3 4 3 4 3 4 = - + - - + - = - - = x x x x x x y y x y . These two functions have the same slope. Two parallel lines do not have an intersection point. (b). If the slopes of two linear functions are different, they have an intersection point. Question 2 (PPF, comparative and absolute advantage). Country A and country B have the same amount of resources, and they produce only food and books. The following two graphs depict Country A and Country B’s production possibility frontiers. 1
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(a). For each country, what is the opportunity cost of producing one unit of food? For each country, what is the opportunity cost of producing one book?
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