Handout 1 (Math Review, Introduction to Economics, Absolute/Comparative Advantage, PPF) This week, you will learn: - Essential Mathematics Review (Chapter 1) o Line and Equation of a Line o Solving Two Equations (will be covered along with market equilibrium) o Percentages (will be covered along with elasticities) o Area of Triangle, Rectangle, and Trapezoid - Basic Economics (Chapter 1 & 2) o Opportunity Cost o Absolute Advantage and Comparative Advantage o Production Possibilities Frontier (PPF) ESSENTIAL MATHEMATICS REVIEW This handout goes over “almost” all of the mathematics required to succeed in ECON 101. It will be helpful to understand what goes through this handout in a step-by-step manner. You should be able to work with these problems as you will be using the concepts and techniques all of the time in this course. Note further that calculators of any types are strictly forbidden in exams. So make sure that you are comfortable with calculations by hand, with precision and reasonable pace. Line and Equation of a Line 1. Find the equation of a line going through (1, -3) with a slope of 3. Plot this line. 2. Find the equation of a line going through (0, 4) and (–2, 6). Plot this line. 3. Consider a line given by the equation y = 3x. a) If it is shifted up by 2 units, what is the new equation of this line? Plot this shifted line alongside the original line. b) Repeat part a) if instead the line is shifted to the left by 2 units. 4. Repeat question 3a) and 3b) when the original equation of a line is y = –3x. 5. Repeat question 3a) and 3b) when the original equation of a line is y = 0.5x + 5. 6. Suppose y is the distance travelled in miles, and x is the time travelled in hours. If the relationship between distance and time is given by equation y = 100x, what is the unit of the slope? Percentages 7. Alice has received her salary raise from $10 to $12.5, what is the percentage change in her salary? What about Bryan who has received his salary cut from $12.5 to $10? Area of Triangle, Rectangle, and Trapezoid 8. What is the area of a triangle with the base of 3 units and height of 6 units? 9. What is the area of a rectangle with the width of 4 units and height of 8 units? 10. What is the area of a trapezoid with the parallel legs of length 10 and 8 units and height of 6 units? “There is no Royal Road to geometry.” – Euclid’s reply to King Ptolemy 1 BASIC ECONOMICS Positive vs. Normative Statements 1. Which of the following questions requires a positive answer? a. What fraction of the population is willing to save more if the government decides to cut income taxes by 10 percent this year? b. What should the government set as the maximum budget for the new legislation for its war on drugs? c. Why should the state of Wisconsin lower the minimum drinking age by 2 years? d. Where should we go after this BLC session? Opportunity Cost 2. Annual college tuition at UW-Madison, including textbooks, is $25,000. It costs $10,000 per year to live Madison. What are the opportunity costs for Alex and Bobby if: a. Alex from Green Bay, WI – he would have earned $30,000 per year from family business in Green Bay? b. Bobby from Madison, WI – he would have earned $30,000 per year from buzzing tables in Madison? Absolute Advantage vs. Comparative Advantage 3. Suppose in 5 hours, Eugene can cook 10 meals or clean 5 cars, while Jonas can cook 6 meals or clean 9 cars. a. Who has the absolute advantage in cooking meals? What about cleaning cars? b. Suppose instead that in 10 hours, Jonas can cook 12 meals or clean 18 cars. Would this change any information of the problem? c. Find the opportunity costs of cooking meals and cleaning cars for each person. d. Who has the comparative advantage in cooking meals? What about cleaning cars? e. Put meals (M) on vertical axes, plot the production possibility frontiers (PPFs) for both Eugene and Jonas. Write down the equations for both. f. If both are only cooking meals now and one car is needed to be cleaned, who should be cleaning the first car? g. (Optional) In light of your finding in 3f), plot the global PPF, that is, combine both Eugene’s and Jonas’ PPFs. 4. It takes 5 minutes for Ryan to pick a coconut and 10 minutes to catch a fish. For Jenny, it takes 6 minutes to pick a coconut and 15 minutes to catch a fish. a. In one hour, how many coconuts can Ryan pick if he does not catch any fish? How many fish can Ryan catch if he does not pick coconuts? What about Jenny? b. Find the opportunity costs of picking a coconut and catching fish for each person. c. Who has the comparative advantage in picking coconuts? What about catching fish? d. Put coconuts (C) on vertical axes, plot the production possibility frontiers (PPFs) for both Eugene and Jonas. Write down the equations for both. Interpret the result with Marginal Rates of Transformation (MRT) 5. Abby and Gale make xylophones (x) and yarn (y) according to the PPFs given by y = 18 – 3x and y = 12 – 6x, respectively. List the opportunity costs each of them face. 2