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UW-Madison ECON 101 - homework 1

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Economics 101Spring 2021Homework #1Due: Thursday, February 11, 2021Math Review1. a. Suppose you know that the two points (X, Y) = (12, 6) and (15, 3) sit on the same line. From this information write an equation for this line in slope-intercept form. b. Suppose that you know that the slope of the line is 5 and that this line also contains the point (20, 25). What is the y-intercept for this line? Show your work. c. You are given the following two equations: Y = 10X + 100 Y = 76 – 2X Find the solution (X, Y) for where these two equations intersect. Show your work. d. Suppose that you know that the relationship between X and Y, where X is the variable measured on the horizontal axis, can be described by the following equation: X = 40 – 2Y for all values of X ≥ 0 You are then told that for every Y value the X value has now increased by 10 units. Write the equation in slope-intercept form for this new line. Show your work. Hint: you might find it helpful to draw a "sketch" illustrating these two lines before you start doing your calculations. e. Suppose that you know that the relationship between X and Y, where X is the variable measured on the horizontal axis, can be described by the following equation: Y = -10 + 4X for all values of X ≥ 0You are then told that for every X value the Y value has now increased by 20 units. Write the equation in slope-intercept form for this new line. Show your work. Hint: you might find it helpful to draw a "sketch" illustrating these two lines before you start doing your calculations. 2. Consider the following equations of two straight linesFirst Set of Equations: y = x/5 + 4 and 0.2y = 4 – xSecond Set of Equations: y = 7x + 1 and y = 7x + 2 1Answer the following questions for each of the above 2 sets of equations. Start with the two equations given as the First Set of Equations and answer the next three questions; then, repeat forthe two equations given in the Second Set of Equations.a. What are the slopes, x-intercept and y-intercept of both lines for each set of equations? b. For each set of equations, graph the two lines in a single graph measuring y on the vertical axis and x on the horizontal axis.c. At which co-ordinate point (x, y) do the two straight lines intersect for each set of equations? [Hint: Be careful on this step when you are working with the equations given as the Second Set of Equations.] PPF Basics3. Megan makes casseroles (C, where C is measured as dozens of casseroles) and pies (P). She has a total of forty hours each week that she can devote to the production of these two items. Thefollowing table provides you with information about Megan’s ability to produce these casseroles and pies. Number of Hours Needed to Make a Dozen Casseroles½ HourNumber of Hours Needed to Make a Pie1 Houra. Given the above information draw Megan’s production possibility frontier (PPF) for casseroles(measured in dozens) and pies per week. Measure Casseroles on the x axis and Pies of the y axis.In your graph label all intercepts. b. Write an equation for Megan’s PPF in slope intercept form. c. For each of the following coordinate pairs of (Dozens of Casseroles, Pies) determine whether the point sits on Megan’s PPF, lies beyond Megan’s PPF, or lies inside Megan’s PPF. Coordinates for each point: (Dozens of Casseroles, Pies)Where Point Lies with respect to Megan’s PPF(60, 12)(50, 14)(48, 18)(12, 37)(20, 30)d. In the table below provide the missing values based on the above information. 2Coordinates for each point: (Casseroles, Pies) Where Point Lies with respect to Megan’s PPF(48, y) Beyond the PPF(15, z) On the PPF(4, w) Inside the PPF(a, 35) On the PPF(d, 19) On the PPFe. What is Megan’s opportunity cost of producing 1 pie? What is Megan’s opportunity cost of producing 10 pies? What is Megan’s opportunity cost of producing 6 dozen casseroles?f. Suppose that Megan gets additional casserole pans and she now finds that she can make 2 dozen casseroles in ½ hour. Nothing else changes in this problem. What is Megan’s opportunity cost of producing one dozen casserolse now? What is Megan’s opportunity cost of producing onepie now?PPF: joint PPF and trading range of prices4. Meg and Pete produce two goods: casseroles (B) and pies (P). Meg and Pete have the same amount of resources available to them. If Meg uses all of her resources to produce casseroles she can produce 20 casseroles and if she uses all of her resources to produce pies she can produce 10 pies; and if Pete uses all of his resources to produce casseroles he can produce 40 casseroles and if he uses of his resources to produce pies he can produce 30 pies. Assume that both Meg and Pete have linear production possibility frontiers. a. Draw a graph that represents Meg’s production possibility frontier given the above information. Measure casseroles on the vertical axis and pies on the horizontal axis. b. Write an equation for Meg’s production possibility frontier given the above information. Writethis equation in slope intercept form. Then fill in the following table using this equation. Pies Produced by Meg Casseroles Produced by Meg24879c. Draw a graph that represents Pete’s production possibility frontier given the above information. Measure casseroles on the vertical axis and pies on the horizontal axis. 3d. Write an equation for Pete’s production possibility frontier given the above information. Determine for each of the following combinations of (casseroles, pies) whether the combination lies on Pete’s PPF, lies inside Pete’s PPF, or lies beyond Pete’s PPF. Combination of (Casseroles, Pies)Location of Combination Relative to Pete’s PPF(36, 3)(33, 6)(22, 12)(24, 15)(2, 27)e. Given the above information, who has the absolute advantage in the production of casseroles? Explain your answer. f. Given the above information, who has the comparative advantage in the production of casseroles? Explain your answer. g. Draw Meg and Pete’s joint PPF. Measure casseroles on the vertical axis and pies on the horizontal axis. Identify any intercepts as well as the coordinates for any “kink” points. Write an equation in slope intercept form for every segment of this joint PPF and provide the relevant range for each segment. h. What is the acceptable range of trading prices in terms of pies for 10 casseroles? Illustrate this using the number line approach presented in class. Make sure to include the arrows and labels that indicate Pete’s perspective


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