ECON 103, 2008-2 ANSWERS TO HOME WORK ASSIGNMENTS Due the Week of May 12 Chapter 1 WRITE [7] Suppose you won $15 on a Lotto Canada ticket at the local 7-Eleven and decided to spend all the winnings on candy bars and bags of peanuts. The price of candy bars is $.75 and the price of peanuts is $1.50. a) Construct a table showing the alternative combinations of the two products that are available. b) Plot the data in your table as a budget line in a graph. What is the slope of the budget line? What is the opportunity cost of one more candy bar? Of one more bag of peanuts? Do these opportunity costs rise, fall, or remain constant as each additional unit of the product is purchased. c) How, in general, would you decide which of the available combinations of candy bars and bags of peanuts to buy? d) Suppose that you had won $30 on your ticket, not $15. Show the $30 budget line in your diagram. Why would this budget line be preferable to the old one? Ans: (a) Consumption alternatives (b) Bags of Peanuts Goods A B C D E F Candy bars 0 4 8 12 16 20 Bags of peanuts 10 8 6 4 2 0 10 Slope.75 1.5.5 20 Candy Bars The slope for the budget line above, with candy bars on the horizontal axis, is -0.5 (= -P cb /P bp ). Note that the figure could also be drawn with bags of peanuts on the horizontal axis. The slope of that budget line would be -2. The opportunity cost of one more candy bar is ½ of a bag of peanuts. The opportunity cost of one more bag of peanuts is 2 candy bars. These opportunity costs are constant. They can be found by comparing any two of the consumption alternatives for the two goods. (c) The decision of how much of each to buy would involve weighing the marginal benefits and marginal costs of the various alternatives. If, for example, the marginal benefits of moving from alternative C to alternative D are greater than the marginal costs, then this consumer should move to D (and then compare again with E, and so forth, until MB=MC is attained). (d) page 1
B ags of P eanuts Income = $15 20 10 Income = $30 20 40 Candy Bars The budget line at $30 would be preferable because it would allow greater consumption of both goods. WRITE [10] Below is a production possibilities table for consumer goods (automobiles) and capital goods (forklifts). Production Alternatives Type of Production A B C D E Automobiles 0 2 4 6 8 Forklifts 30 27 21 12 0 a) Show these data graphically. Upon what specific assumptions is this production possibilities curve based? b) If the economy is at point C, what is the cost of one more automobile? Of one more forklift? Explain how the production possibilities curve reflects the law of increasing opportunity costs. c) If the economy characterized by this production possibilities table and curve were producing 3 automobiles and 20 fork lifts, what could you conclude about its use of available resources? d) What would production at a point outside the production possibilities curve indicate? What must occur before the economy can attain such a level of production? Ans: a. See the curve. The assumptions are full employment, fixed supplies of resources, fixed technology and two goods. b. 4.5 forklifts;.33 automobiles, as determined from the table. Increasing opportunity costs are reflected in the concave-from-the-origin shape of the curve. This means the economy must give up larger and larger amounts of rockets to get constant added amounts of automobiles and vice versa. c. The economy is underutilizing its available resources. The assumption of full employment has been violated. d. Production outside the curve cannot occur (consumption outside the curve could occur through foreign trade). To produce beyond the current production possibilities curve this economy must realize an increase in its available resources and/or technology. page 2
AUTOMOBILES 8 E 6 D 4 C 2 B 10 20 30 A ROCKETS CONSIDER [1] What is an opportunity cost? How does the idea relate to the definition of economics? Which of the following decisions would entail the greatest opportunity cost: Allocating a square block in the heart of Toronto for a surface parking lot or allocating a square block at the edge of a typical suburb for such a lot? Explain. Ans: An opportunity cost is what was sacrificed to do or acquire something else. The condition of scarcity creates opportunity cost. If there were no scarcity, there would be no need to sacrifice one thing to acquire another. The opportunity cost would be much higher in Toronto as the alternative uses for that square block are much more valuable than for a typical suburban city block. page 3
Capital goods Capital goods CONSIDER [14] On average, households in China save 40 percent of their annual income each year, whereas households in the Canada save less than 5 percent. Production possibilities are growing at roughly 9 percent annually in China and 3.5 percent in Canada. Use graphical analysis of present goods versus future goods to explain the differences in growth rates. Ans:The figures below reflect the situation. China s production possibilities curve lies far to the right of Canada s (China is a much bigger economy). A significant portion of savings goes into investment in capital goods (future goods). As a percentage of total output, China produces fewer consumer goods (present goods) and more capital goods than Canada. As a result, China s future production possibilities will shift out faster than Canada s. Canada China 2020 X 2020 2007 2007 X Consumer goods Consumer goods page 4
Chapter 1, Appendix WRITE [3] The following table contains data on the relationship between saving and income. Rearrange these data into a meaningful order and graph them on the accompanying grid. What is the slope of the line? The vertical intercept? Interpret the meaning of both the slope and the intercept. Write the equation that represents this line. What would you predict saving to be at the $12,500 level of income? Ans. Arrange the values from low income to high income. Income/year Saving/year 0-500 5,000 0 10,000 500 15,000 1,000 20,000 1,500 The slope of the relationship between income and savings is 0.1. That is, if income goes up by y, savings goes up by (0.1)*y. The vertical intercept is -500. The slope is the amount by which savings will increase for a $1 increase in income. The intercept is the amount of savings (or disavings in this case) at zero income. Equation is S= (-500) + (0.1)*y where S = savings and y = income. Savings will be 750 at the 12,500 income level. WRITE [4] Construct a table from the data shown on the graph below. Which is the dependent variable and which the independent variable? Summarize the data in equation form. Ans. Here is the table. Exam score 10 0 20 1 30 2 40 3 etc etc Study time Note: the table is not accurate for this course. You won't get 100% by studying just 9 hours. The independent variable is your study time, the dependant variable is your exam score. The dependent variable is the exam score (it depends upon the amount of time spent studying). If S = score and T = time, then S = 10 + (10)*T WRITE [7] The accompanying graph shows curve XX' and tangents at points A, B, and C. Calculate the slope of the curve at these three points. Ans. Slopes: at A = +4; at B = 0; at C =-4. WRITE: Use a sheet of graph paper to answer the following question: a. You have to sleep 8 hours a day. The remainder of the day you can divide between studying and leisure. Let leisure hours be the x variable and study hours be the Y variable. Plot the relationship between combinations of X and Y on your graph paper. Ans: If you sleep for 8 hours, this leaves 16 hours (24 hours in a day minus 8 hours for sleep) to divide between study and leisure. The combinations of study and leisure are shown by the dark solid line in the diagram. page 5
Study hours b. What is the slope of the line that shows the relationship between study hours and leisure hours? Ans: Slope = -1. You must give up one hour of leisure for one hour of study. c. You catch the flu and Health Services orders you to get 10 hours sleep a night. Draw the new relationship between study and leisure. What is the slope of this line? Ans: Your non-sleep time possibilities shifts in from 16 hours to 14 hours. The slope is still -1. d. Now assume that if you don t study at all you only need 4 hours of sleep (because your leisure activities are sun-bathing and lying on the couch watching videos) But, for every hour that you study, you need an extra 15 minutes of sleep (i.e., 0.25 of an hour). Plot the relationship between combinations of X and Y on your graph paper. What is the slope of this line? Ans If you do not study at all, you will have 20 hours of leisure.but for each study hour you must give up 1.25 hours of leisure. If you only study and sleep, you can study for 16 hours and sleep for 8 hours. The slope of the line is (1/1.25) = -(0.8). 16 14 14 16 20 Leisure hours page 6