answerstohomework1spring2010

answerstohomework1spring2010 - Economics 102 Spring 2010...

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Economics 102 Spring 2010 Home Assignment #1 (ANSWER KEY) Due 2/3/10 at lecture Directions: The homework will be collected in a box before the lecture. Please place your name , TA name and section number on top of the homework (legibly). Make sure you write your name as it appears on your ID so that you can receive the correct grade. Please remember the section number for the section you are registered, because you will need that number when you submit exams and homework. Late homework will not be accepted so make plans ahead of time. Please show your work . Good luck! Problem 1. Find the intersection of the two lines, described by the following equations: x + y = 10 y = 2x – 5 Solution. We solve for y in both equations: y = 10 – x y = 2x – 5, then equate the right sides to solve for x: 10 – x = 2x – 5 15 = 3x x = 5, which implies y = 10 – x = 5. The answer is (5,5). Problem 2. (a) Find the equation of the line which goes through the origin and the point (2,8). (b) Find the equation of a line that has a y-intercept of -5 and is parallel to the line you found in part (a). Solution. (a) The slope of the line is y x 8 0 2 0 8 2 4 , hence the equation of the line is y = 4x + b. Since it goes through the origin, b = 0, so the answer is y = 4x. (b) Parallel lines have the same slope, so the equation we’re looking for has the same form of y = 4x+b. The y-intercept of -5 means at x = 0 y = -5, but y(0) = b, hence b = -5 and the equation is y = 4x-5. Problem 3. A farm in Madison produces two goods, milk and corn. The farm’s production possibilities frontier can be represented as a linear line where corn is measured on the X axis and milk is measured on the Y axis. The points (2, 10) and (4, 6) are on the farm’s linear PPF. (a) What is the slope-intercept form of the straight line that expresses the farm’s PPF?
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(b) Assume this farm is producing on its PPF. How many units of milk will the farm produce if it produces 3 units of corn? (c) Assume this farm is producing on its PPF. How many units of corn will the farm produce if it produces 0 units of milk? Solution. (a) (2, 10) and (4, 6) are on the PPF, so the slope of the PPF is (6-10) / (4-2) = -2, so the straight line should be Y = -2X + a , where a is unknown. Now we plug in point (4, 6), we can get 6 = -2 * 4 + a , and solving for a , we find that a = 14. So the Straight line should be Y = -2X +14. (b) If this farm produces 3 units of corn, then X = 3, so Y= -2 * 3 + 14 = 8, so the farm would produce 8 units of milk. (c) If the farm produces 0 units of milk, Y = 0, so 0 = -2X +14. X = 7. 7 units of corn will be produced.
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This note was uploaded on 05/27/2011 for the course ECON 201 taught by Professor Caltech during the Spring '10 term at Wisc Eau Claire.

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answerstohomework1spring2010 - Economics 102 Spring 2010...

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