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UW-Madison ECON 101 - Homework

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Economics 101Summer 2008Homework #1Please make sure your homework includes your name and the time and day of your discussion section. In addition, please write legibly and neatly and make sure your answer is clearly marked (you might place a box around your answer). Homework shouldbe stapled (there is no stapler at the lecture), and it should be neat. All homework must beturned in on the date it is due in the large lecture and it must be turned in at the beginning of the lecture. No late homework assignments will be accepted. Note: Homework #1 includes a review of some basic math principles that we use throughout the course. Show your work and do not use a calculator in doing these problems.1. For this question you are given information about the linear relationship between two variables. Write an equation in slope-intercept form expressing this relationship. a. B and C are two variables that are linearly related to one another and variable C is measured on the y-axis. You are given two points on the line and the coordinates of these two points are (10, 5) and (20, 10).b. X and Y are linearly related to one another. One point on this line is (100,2000) and theslope of the line is -100. Y is measured on the vertical axis.c. P and Q are linearly related to one another with P measured on the y axis. The slope of this relationship is -10 and the x-intercept is 500.d. W and V are linearly related to one another with V measured on the y-axis. The midpoint of this line is (200,100) and every time W increases by 50 units, V decreases by 25 units. 2. For each set of equations below find the equilibrium values for the two variables. a. X = 100 – 2Y X = 500 – 4Yb. Y = 500 – 4X Y = Xc. P = 4000 – Q, where Q is measured on the horizontal axis P = 2000 + Qd. Q = 1000 – 2P, where Q is measured on the horizontal axis Q = 500 + 6P3. The percentage change in a variable is equal to the {[(new measure of the variable) – (initial measure of the variable)]/(initial measure of thevariable)}*100.a. Suppose the initial value of X is 80 in 2006 and that X increases by 20 points in 2007. Calculate the percentage change in X between 2006 and 2007.b. Suppose the value of X in 2007 is 100 and that X decreases by 25% in 2008. Calculate the value of X in 2008.c. Suppose P decreases by 10% while Q increases by 100%. The initial values of P and Q,respectively, are 10 and 100. What are the new values of P and Q?4. The following table describes the production possibility frontier (PPF) for 2008 for Littleton, a community that produces two goods, food and clothing, from its available resources and technology. Assume Littleton’s PPF is linear between the points listed in the table. Points on Little’s PPF Food (Pounds of Food) Clothing (# of Items)A 0 1000B 100 950C 400 750D 600 450E 700 100F 725 0a. Draw a graph of Littleton’s PPF for 2008 based on the information in the above table. In your graph, measure food (F) on the vertical axis and clothing (C) on the horizontal axis. b. Suppose Littleton is currently producing at point C on their PPF. What is the opportunity cost to Littleton of producing one additional unit of food?c. Suppose Littleton is currently producing at point C. What is the opportunity cost of producing one additional unit of clothing?d. Suppose Littleton is currently producing at point E. What is the opportunity cost of producing 25 more units of food?e. Suppose Littleton is currently producing at point E. What is the opportunity cost of producing 650 more units of clothing? f. Does Littleton’s PPF illustrate the Law of Increasing Opportunity Cost with regard to food production? Explain your answer.g. Does Littleton’s PPF illustrate the Law of Increasing Opportunity Cost with regard to clothing production? Explain your answer.h. For each of the following combinations of (C, F) identify whether the combination is on Littleton’s PPF, lies inside Littleton’s PPF, or lies beyond or outside Littleton’s PPF. Explain your answer. i. (1050, 20)ii. (800, 125)iii. (725, 300)iv. (400, 550)5. Roger and Marie both like home cooked meals and hand knit sweaters. Suppose that Roger and Marie have the same amount of time to devote to each of these pursuits and that they currently do not trade with one another. The table below provides information about the maximum amount of meals and sweaters Roger and Marie can produce if theyuse all of their resources to produce either meals or sweaters. Assume that Roger and Marie’s production possibility frontiers are linear. Home Cooked Meals Hand Knit SweatersRoger 20 10Marie 16 6a. Who has the absolute advantage in producing meals? Who has the absolute advantage in producing sweaters?b. What is Roger’s opportunity cost of producing one additional sweater? What is Roger’s opportunity cost of producing one additional meal?c. What is Marie’s opportunity cost of producing one additional sweater? What is Roger’sopportunity cost of producing one additional meal?d. Suppose Roger and Marie decide to specialize and trade. What good should Roger specialize in producing? Explain your answer.e. Suppose Roger and Marie decide to specialize and trade. What good should Marie specialize in producing? Explain your answer.f. What is the range of prices in terms of sweaters that one meal will trade for if Marie and Roger specialize?g. What is the range of prices in terms of meals that one sweater will trade for if Marie and Roger specialize?6. Sarah and Renee produce clothing and food. The table below provides information on the number of hours of labor that a unit of clothing or a unit of food takes Sarah or Renee to produce. Assume that Sarah and Renee use only labor to produce clothing and food. Assume that the production possibility frontiers for both Sarah and Renee are linear. Hours of Labor Needed toProduce One Unit ofClothingHours of Labor Needed toProduce One Unit of FoodSarah 4 2Renee 3 2a. What is the opportunity cost of producing one unit of clothing for Sarah?b. What is the opportunity cost of producing one unit of food for Sarah?c. What is the opportunity cost of producing one unit of clothing for Renee?d. What is the opportunity cost of producing one unit of food for Renee?e. Suppose Sarah and Renee decide to specialize and trade with one another. What good should Sarah specialize in producing? Explain your answer.f. What is a range of prices in terms of food that one unit of clothing will trade for if Sarah and Renee


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UW-Madison ECON 101 - Homework

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