This Document Contains Chapters 1 to 2 First Principles Chapter 1. In each of the following situations, identify which of the twelve principles is at work. a. You choose to purchase your textbooks online through Chegg rather than paying a higher price for the same books through your college bookstore. b. On your spring break trip, your budget is limited to $35 a day. c. Craigslist allows departing students to sell items such as used books, appliances, and furniture rather than giving them away as they formerly did. d. After a hurricane did extensive damage to homes on the island of St. Crispin, homeowners wanted to purchase many more building materials and hire many more workers than were available on the island. As a result, prices for goods and services rose dramatically across the board. e. You buy a used textbook from your roommate. Your roommate uses the money to buy songs from iTunes. f. You decide how many cups of coffee to have when studying the night before an exam by considering how much more work you can do by having another cup versus how jittery it will make you feel. g. There is limited lab space available to do the project required in Chemistry 101. The lab supervisor assigns lab time to each student based on when that student is able to come. h. You realize that you can graduate a semester early by forgoing a semester of study abroad. i. At the student center, there is a bulletin board on which people advertise used items for sale, such as bicycles. Once you have adjusted for differences in quality, all the bikes sell for about the same price. j. You are better at performing lab experiments, and your lab partner is better at writing lab reports. So the two of you agree that you will do all the experiments, and she will write up all the reports. k. State governments mandate that it is illegal to drive without passing a driving exam. l. Your parents’ after-tax income has increased because of a tax cut passed by Congress. They therefore increase your allowance, which you spend on a spring break vacation. 1. a. People usually exploit opportunities to make themselves better off. In this case, you make yourself better off by buying textbooks at a lower price. b. Resources are scarce. Since you have only $35 a day, your resources are limited (scarce). c. Markets usually lead to efficiency. The market here is represented by the buyers and sellers who use Craigslist to trade goods, in contrast to the “nonmarket” of simply giving items away to one’s roommate. The market is efficient because it enables people who want to sell items to find those who want to buy those items. This is in contrast to a system in which items are simply left with a roommate, who may have little or no desire to have them. d. Overall spending sometimes gets out of line with the economy’s productive capacity. The spending by St. Crispin homeowners on building materials and workers fell short of the economy’s ability to produce those goods and services. As a result, prices on the island rose across the board (inflation). e. One person’s spending is another person’s income. Your spending on the used textbook is your roommate’s income. Chapter 1 f. “How much” is a decision at the margin. Your decision is one of “how much” coffee to consume, and you evaluate the trade-off between keeping yourself awake and becoming more jittery from one more cup of coffee. g. Resources should be used as efficiently as possible to achieve society’s goals. Allocating scarce lab space according to when each student can use that space is efficient. h. The real cost of something is what you must give up to get it. The real cost of a semester abroad is giving up the opportunity to graduate early. i. Markets move toward equilibrium. Any bicycle a buyer chooses will leave him or her equally well off. That is, a buyer who chooses a particular bicycle cannot change actions and find another bicycle that makes him or her better off. Also, no seller can take a different action that makes him or her better off: no seller can charge a higher price for a bicycle of similar quality, since no one would buy that bicycle. j. There are gains from trade. If each person specializes in what he or she is good at (that is, in comparison with others that person has an advantage in producing that good), then there will be gains from specialization and trade. k. When markets don’t achieve efficiency, government intervention can improve society’s welfare. Unsafe drivers don’t take into account the dangers they pose to others and often to themselves. So when unsafe drivers are allowed to drive, everyone is made worse off. Government intervention improves society’s welfare by assuring a minimum level of competence in driving. l. Government policies can change spending. In this case, a tax cut has increased spending. 2. Describe some of the opportunity costs when you decide to do the following. a. Attend college instead of taking a job b. Watch a movie instead of studying for an exam c. Ride the bus instead of driving your car 2. a. One of the opportunity costs of going to college is not being able to take a job. By choosing to go to college, you give up the income you would have earned on the job and the valuable on-the-job experience you would have acquired. Another opportunity cost of going to college is the cost of tuition, books, s upplies, and so on. Alternatively, the benefit of going to college is being able to find a better, more highly paid job after graduation, in addition to the joy of learning. b. Watching the movie gives you a certain benefit, but allocating your time (a scarce resource) to watching the movie also involves the opportunity cost of not being able to study for the exam. As a result, you will likely get a lower grade on the exam—and all that that implies. c. Riding the bus gets you where you need to go more cheaply than, but probably not as conveniently as, driving your car. That is, some of the opportunity costs of taking the bus involve waiting for the bus, having to walk from the bus stop to where you need to go rather than parking right outside the building, and probably a slower journey. If the opportunity cost of your time is high (your time is valuable), these costs may be prohibitive. 3. Liza needs to buy a textbook for the next economics class. The price at the college bookstore is $65. One website offers it for $55, and another site, for $57. All prices include sales tax. The accompanying table indicates the typical shipping and handling charges for the textbook ordered online. Shipping method Delivery time Charge Standard shipping 3–7 days $3.99 Second-day air 2 business days 8.98 Next-day air 1 business day 13.98 a. What is the opportunity cost of buying online instead of at the bookstore? Note that if you buy the book online, you must wait to get it. b. Show the relevant choices for this student. What determines which of these options the student will choose? 3. a. The opportunity cost of buying online is whatever you must give up to get the book online. So the opportunity cost of buying online is the sum of the shipping charges plus the opportunity cost of your time spent waiting for the book to arrive (at the bookstore the book is available immediately) minus the cost saving you receive by buying online versus buying at the bookstore. b. Below is a list of all of Liza’s options and their purely monetary costs: Buy from bookstore $65 Buy from first site (price $55), 1-day delivery $55 + $13.98 = $68.98 Buy from first site (price $55), 2-day delivery $55 + $ 8.98 = $63.98 Buy from first site (price $55), 3- to 7-day delivery $55 + $ 3.99 = $58.99 Buy from second site (price $57), 1-day delivery $57 + $13.98 = $70.98 Buy from second site (price $57), 2-day delivery $57 + $ 8.98 = $65.98 Buy from second site (price $57), 3- to 7-day delivery $57 + $ 3.99 = $60.99 It is clear that Liza would never buy from the second site, where the book costs $57: for each delivery time, she is better off buying the book from the first site, where the book costs $55. It is also clear that she would never buy the book from the first site and have it delivered the next business day: it costs more that way ($68.98) than getting it from the bookstore (assuming that it is costless to get to and from the bookstore). But it is not clear whether she will buy the book from the bookstore or the first site with delivery times of 2 or 3–7 days: this depends on her opportunity cost of time. The higher the cost of waiting, the more likely she is to buy the book from the bookstore, where she does not need to wait. 4. Use the concept of opportunity cost to explain the following. a. More people choose to get graduate degrees when the job market is poor. b. More people choose to do their own home repairs when the economy is slow and hourly wages are down. c. There are more parks in suburban than in urban areas. d. Convenience stores, which have higher prices than supermarkets, cater to busy people. e. Fewer students enroll in classes that meet before 10:00 a.m . 4. a. The worse the job market, the lower the opportunity cost of getting a graduate degree. One of the opportunity costs of going to graduate school is not being able to work. But if the job market is bad, the salary you can expect to earn is low or you might be unemployed—so the opportunity cost of going to school is also low. b. When the economy is slow, the opportunity cost of people’s time is also lower: the wages they could earn by working longer hours are lower than when the economy is booming. As a result, the opportunity cost of spending time doing your own repairs is lower—so more people will decide to do their own repairs. c. The opportunity cost of parkland is lower in suburban areas. The price per square foot of land is much higher in urban than in suburban areas. By creating parkland, you therefore give up the opportunity to make much more money in cities than in the suburbs. d. The opportunity cost of time is higher for busy people. Driving long distances to supermarkets takes time that could be spent doing other things. Therefore, busy people are more likely to use a nearby convenience store. e. Before 10:00 a.m . the opportunity cost of time for many students is very high—it means giving up an extra hour’s sleep. That extra hour is much more valuable before 10:00 a.m . than later in the day. 5. For the following examples, state how you would use the principle of marginal analysis to make a decision. a. Deciding how many days to wait before doing your laundry b. Deciding how much time to spend researching before writing your term paper c. Deciding how many bags of chips to eat d. Deciding how many class lectures to skip 5. a. Each day that you wait to do your laundry imposes a cost: you have fewer clean clothes to choose from. But each day that you wait also confers a benefit: you can spend your time doing other things. You will wait another day to do your laundry if the benefit of waiting to do the laundry that day is greater than the cost. b. The more research you do, the better your paper will be. But there is also an opportunity cost: every additional hour you spend doing research means you cannot do other things. You will weigh the opportunity cost of doing one more hour of research against the benefit gained (in terms of an improved paper) from doing research. You will do one more hour of research if the benefit of that hour outweighs the cost. c. Each bag of chips you eat gives you a benefit: it satisfies your hunger. But it also has a cost: the money spent for each bag (and, if you are weight-conscious, the additional calories). You will weigh the cost against the benefit of eating one more bag. If the cost is less than the benefit, you will eat that one more bag of chips. d. Each lecture that you skip implies a cost: getting further behind with the material and having to teach it to yourself just before the exam. But each skipped lecture also means you can spend the time doing other things. You will continue to skip lectures if the cost of skipping is lower than the benefit of spending that time doing other things. 6. This morning you made the following individual choices: you bought a bagel and coffee at the local café, you drove to school in your car during rush hour, and you typed your course notes for your roommate because she was texting in class—in return for which she will do your laundry for a month. For each of these actions, describe how your individual choices interacted with the individual choices made by others. Were other people left better off or worse off by your choices in each case? 6. When you bought the bagel and coffee, you paid a price for them. You would not have bought that breakfast if your enjoyment of it (your welfare) had not been greater than the price you paid. Similarly, the café owner would not have sold you the bagel and coffee if the price he received from you were less than the cost to him of making them. This is an example of how everybody gains from trade: both you and the café owner are better off. hen you chose to drive your car during the rush hour, you added to the W congestion on the road. Your choice had a side effect for other motorists: your driving slowed everybody else down just a little bit more. Your choice made other motorists worse off. yping your notes for your roommate in exchange for her doing your laundry T is another example of the gains that come from trade. Both of you voluntarily agreed to specialize in a task that each is comparatively better at because you expected to gain from this interaction. Your choice made both you and your roommate better off. 7. The Hatfield family lives on the east side of the Hatatoochie River, and the McCoy family lives on the west side. Each family’s diet consists of fried chicken and corn-on-the-cob, and each is self-sufficient, raising their own chickens and growing their own corn. Explain the conditions under which each of the following would be true. a. The two families are made better off when the Hatfields specialize in r aising chickens, the McCoys specialize in growing corn, and the two f amilies trade. b. The two families are made better off when the McCoys specialize in raising chickens, the Hatfields specialize in growing corn, and the two families trade. 7. a. Gains from trade usually arise from specialization. If the Hatfields (compared to the McCoys) are better at raising chickens and the McCoys (compared to the Hatfields) are better at growing corn, then there will be gains from specialization and trade. b. Similar to the answer to part a, if the McCoys (compared to the Hatfields) are better at raising chickens and the Hatfields (compared to the McCoys) are better at growing corn, then there will be gains from specialization and trade. 8. Which of the following describes an equilibrium? Which does not? If the situation does not describe an equilibrium, what would an equilibrium look like? a. Many people regularly commute from the suburbs to downtown P leasantville. Due to traffic congestion, the trip takes 30 minutes via highway but only 15 minutes via side streets. b. At the intersection of Main and Broadway are two gas stations. One station charges $3.00 per gallon for regular gas and the other charges $2.85 per g allon. Customers can get service immediately at the first station but must wait in a long line at the second. c. Every student enrolled in Economics 101 must also attend a weekly tutorial. This year there are two sections offered: section A and section B, which meet at the same time in adjoining classrooms and are taught by equally competent instructors. Section A is overcrowded, with people sitting on the floor and often unable to see what is written on the board at the front of the room. Section B has many empty seats. 8. a. This is not an equilibrium. Assume that all people care about is the travel time to work (not, for instance, how many turns they need to make or what the scenery is like). Some people could be better off using the side streets, which would cut down their travel time. Eventually, as the situation moves to equilibrium (that is, as more people use the side streets), travel times on the highway and along the side streets will equalize. b. This might be an equilibrium. Those who buy gas at the first station would be worse off by buying gas at the second if the value of their time spent w aiting exceeded the savings at the pump: they would save 15 cents per gallon but would incur the opportunity cost of waiting in a long line. You should expect very busy people (a high opportunity cost of time) to buy gas at the first station. Those who buy gas at the second station might be worse off by b uying gas at the first: they would not have to wait in line but would pay 15 cents more per gallon. You should expect people with a lot of free time (a low opportunity cost of time) to buy gas at the second station. c. This is not an equilibrium. If students from section A attended section B instead, they would be better off: they could get seats and see the board without incurring any cost (since the section meets at the same time and is taught by an equally competent instructor). Over time, you should expect students to switch from s ection A to section B until equilibrium is established. 9. For each of the following, explain whether you think the situation is efficient or not. If it is not efficient, why not? What actions would make it efficient? a. Electricity is included in the rent at your dorm. Some residents in your dorm leave lights, computers, and appliances on when they are not in their rooms. b. Although they cost the same amount to prepare, the cafeteria in your dorm consistently provides too many dishes that diners don’t like, such as tofu casserole, and too few dishes that diners do like, such as roast turkey with dressing. c. The enrollment for a particular course exceeds the spaces available. Some students who need to take this course to complete their major are unable to get a space even though others who are taking it as an elective do get a space. 9. a. This is not efficient. If the lights were turned off, some students could be made better off without making other students worse off because the college would save money on electricity that it could spend on student programs. By leaving lights and appliances on when leaving their rooms, residents do not take into account the negative side effect they impose on their college—the higher cost of electricity. If students were forced to pay their own individual electricity costs (that is, if they fully took into account the cost of their actions), then they would turn the lights and appliances off when leaving their rooms. This situation would be efficient. b. This is not efficient. Instead of serving dishes that many diners do not like, the cafeteria should serve more of the equal-cost dishes that diners do like. That way, some students could be made better off without other students being made worse off. c. This is not efficient. In an efficient scheme, spaces would be allocated to those students who value them most. In this case, however, some spaces are allocated to students who value them less (those who take the course as an e lective) than other students (those who need the course to graduate). Efficiency could be improved as follows: if a student who is not currently enrolled in the course values it more than a student who is enrolled, then the unenrolled student should be willing to pay the enrolled student to give up his or her space. At some price, this trade would make both students better off and the outcome would be efficient. 10. Discuss the efficiency and equity implications of each of the following. How would you go about balancing the concerns of equity and efficiency in these areas? a. The government pays the full tuition for every college student to study whatever subject he or she wishes. b. When people lose their jobs, the government provides unemployment benefits until they find new ones. 10. a. Although this policy is equitable, it may not be efficient, depending on the beneficial side effects of education. It does allow everyone, regardless of ability to pay, to attend college. But it may not be efficient: subsidizing the full cost of tuition for everyone lowers the opportunity cost of going to college, and this might lead some people to go to college when they could more productively follow a career that does not require a college education. And since resources (including government money) are scarce, paying tuition for these people has an opportunity cost: some other (possibly more worthwhile) government projects cannot be undertaken. One way of getting around this problem is to award scholarships based on academic ability. b. Although this policy may be equitable (it guarantees everyone a certain amount of income), it may not be efficient. People respond to incentives. If unemployment becomes more attractive because of the unemployment benefit, some unemployed people may no longer try to find a job or may not try to find one as quickly as they would without the benefit. Ways to get around this problem are to provide unemployment benefits only for a limited time or to require recipients to prove that they are actively searching for a new job. 11. Governments often adopt certain policies in order to promote desired behaviour among their citizens. For each of the following policies, determine what the incentive is and what behavior the government wishes to promote. In each case, why do you think that the government might wish to change people’s behavior, rather than allow their actions to be solely determined by individual choice? a. A tax of $5 per pack is imposed on cigarettes. b. The government pays parents $100 when their child is vaccinated for measles. c. The government pays college students to tutor children from low-income families. d. The government imposes a tax on the amount of air pollution that a company discharges. 11. a. This policy creates an incentive to smoke less by making a pack of cigarettes more costly. This is exactly what policy makers wish to promote. Cigarettes have undesirable side effects on other people, which smokers do not (or only insufficiently) take into account. One is that other people have to breathe in second-hand smoke. Another is the cost of health care: when smokers who need treatment for lung cancer are covered by Medicare or Medicaid, the rest of society has to foot the bill. Since individuals do not take these costs (costs that arise for other people) into account in deciding whether or not (or how much) to smoke, the amount of cigarettes smoked will be inefficiently high. The tax is a way to make people take these costs into account in deciding whether or not to smoke. b. This policy creates an incentive to have children vaccinated: it increases the benefit to parents from vaccination of their children. Getting vaccinated means not only that a child will not contract the measles but also that he or she cannot pass the measles on to other children. That is, there is a side effect for other people (their children get sick less often) that parents do not take into account in their decision of whether or not to have their own child vaccinated. The $100 payment (a government subsidy) is a way to make individuals take into account in their decisions the benefit they can create for other people. c. This policy creates incentives for low-income families to get college students to tutor their children, since getting a tutor is now cheaper or free. This results in better performance in school by these children and higher levels of educational attainment. This has positive side effects for the rest of society: the better children do in school, the more productive, happier, and healthier citizens they will be. d. This tax creates the incentive to emit fewer air pollutants. Pollution has a negative side effect for others: it decreases air quality (for instance, it contributes to the formation of ozone smog) and results in a variety of health complications (for instance, asthma). In deciding how much pollution to discharge, a company does not take these negative side effects sufficiently into account. The tax is a way to make pollution more expensive, that is, to make the company face the cost it imposes on others. 12. In each of the following situations, explain how government intervention could improve society’s welfare by changing people’s incentives. In what sense is the market going wrong? a. Pollution from auto emissions has reached unhealthy levels. b. Everyone in Woodville would be better off if streetlights were installed in the town. But no individual resident is willing to pay for installation of a streetlight in front of his or her house because it is impossible to recoup the cost by charging other residents for the benefit they receive from it. 12. a. In deciding how much to drive, each driver does not take into account the cost of auto emissions he or she imposes on others. That is, the market will lead to there being too much pollution. One way for governments to intervene would be to tax fuel or to tax cars that get low gas mileage. Or governments could subsidize new and cleaner fuels or technologies, such as hybrid cars. This would create incentives for people to switch to cars that use less polluting gas or to drive less. b. The market in this situation leads to too few (or no) streetlights in Woodville. Governments could improve residents’ welfare by paying for streetlight installation from the taxes paid by residents. 13. Tim Geithner, a former U.S. Treasury Secretary, has said, “The recession that began in late 2007 was extraordinarily severe,” he declared, “but the actions we took at its height to stimulate the economy helped arrest the freefall, preventing an even deeper collapse and putting the economy on the road to recovery. Which two of the three principles of economy-wide interaction are at work in this statement? 13. The Obama stimulus is an example of government policy aimed at changing spending: by cutting taxes and also by directly increasing government spending, the package sought to boost overall spending in the economy. And as spending rises, firms increase production. This is an example of the principle that one person’s spending is another person’s income. 14. A sharp downturn in the U.S. housing market in August 2007 reduced the income of many who worked in the home construction industry. A Wall Street Journal news article reported that Walmart’s wire-transfer business was likely to suffer because many construction workers are Hispanics who regularly send part of their wages back to relatives in their home countries via Walmart. With this information, use one of the principles of economy-wide interaction to trace a chain of links that explains how reduced spending for U.S. home purchases is likely to affect the performance of the Mexican economy. 14. The correct principle in this case is that one person’s spending is another person’s income. Here, a reduction in spending for U.S. home purchases leads to a fall in the income of workers in the home construction industry. This, in turn, leads to a reduction in funds sent by workers to relatives in Mexico, which leads to a reduction in spending by Mexican households. This, in turn, leads to less business for Mexican firms and job losses in Mexico. Ultimately, the Mexican economy is likely to be adversely affected by the downturn in the U.S. housing market. 15. In October 2015, Hurricane Joaquin caused massive destruction to North and South Carolina, New York, and Florida. Catastrophic flooding occurred with hundreds of people requiring rescue, 25 killed, and estimated damage of $12 billion. Even those who weren’t directly affected by the destruction were hurt because businesses and jobs dried up. Using one of the principles of economywide interaction, explain how government intervention can help in this situation. 15. The destruction caused by Hurricane Joaquin caused a reduction in spending by residents in the area. This, in turn, led to reduced income as businesses failed or contracted and employment suffered. The government can help remedy the situation by spending more in the area—say, by employing people for cleanup and construction—to counterbalance the reduced spending by private residents. This is an example of the principle that government policies can change spending. 16. During the Great Depression, food was left to rot in the fields or fields that had once been actively cultivated were left fallow. Use one of the principles of economy-wide interaction to explain why. 16. During the Great Depression, spending fell far short of the country’s capacity to produce. This reflects the principle that overall spending sometimes gets out of line with the economy’s productive capacity. As a result of the plunge in spending during the Great Depression, farmers could not find enough buyers for food that had already been produced, so it was left to rot. Likewise, some farmers left their fields fallow. Economic Models: Trade-offs and Trade 1. Two important industries on the island of Bermuda are fishing and tourism. According to data from the Food and Agriculture Organization of the United Nations and the Bermuda Department of Statistics, in 2014 the 315 registered fishermen in Bermuda caught 497 metric tons of marine fish. And the 2,446 p eople employed by hotels produced 580,209 hotel stays (measured by the number of visitor arrivals). Suppose that this production point is efficient in production. Assume also that the opportunity cost of 1 additional metric ton of fish is 2,000 hotel stays and that this opportunity cost is constant (the opportunity cost does not change). a. If all 315 registered fishermen were to be employed by hotels (in addition to the 2,446 people already working in hotels), how many hotel stays could Bermuda produce? b. If all 2,446 hotel employees were to become fishermen (in addition to the 315 fishermen already working in the fishing industry), how many metric tons of fish could Bermuda produce? c. Draw a production possibility frontier for Bermuda, with fish on the horizontal axis and hotel stays on the vertical axis, and label Bermuda’s actual production point for the year 2014. 1. a. Forgoing the production of 1 metric ton of fish allows Bermuda to produce 2,000 additional hotel stays. Therefore, forgoing the production of 497 metric tons of fish allows Bermuda to produce 2,000 × 497 = 994,000 additional hotel stays. If all fishermen worked in the hotel industry, Bermuda could produce 580,209 + 994,000 = 1,574,209 hotel stays. b. Forgoing the production of 2,000 hotel stays allows Bermuda to produce 1 additional metric ton of fish, so giving up 580,209 hotel stays allows Bermuda to produce 580,209/2,000 = 290.1 additional metric tons of fish. If all hotel employees worked in the fishing industry, Bermuda could produce 497 + 290.1 = 787.1 metric tons of fish. c. The accompanying diagram shows the production possibility frontier for Bermuda. Note that it is a straight line because the opportunity cost is constant. Point A is Bermuda’s actual p roduction point. Quantity of hotel stays (thousands) 1,574.2 580.2 A Bermuda PPF 0 497 787.1 Quantity of fish (metric tons) Chapter 2 2. According to data from the U.S. Department of Agriculture’s National Agricultural Statistics Service, 124 million acres of land in the United States were used for wheat or corn farming in a recent year. Of those 124 million acres, farmers used 50 million acres to grow 2.158 billion bushels of wheat and 74 million acres to grow 11.807 billion bushels of corn. Suppose that U.S. wheat and corn farming is efficient in production. At that production point, the opportunity cost of producing 1 additional bushel of wheat is 1.7 fewer bushels of corn. However, because farmers have increasing opportunity costs, additional bushels of wheat have an opportunity cost greater than 1.7 bushels of corn. For each of the following production points, decide whether that production point is (i) feasible and efficient in production, (ii) feasible but not efficient in production, (iii) not feasible, or (iv) unclear as to whether or not it is feasible. a. Farmers use 40 million acres of land to produce 1.8 billion bushels of wheat, and they use 60 million acres of land to produce 9 billion bushels of corn. The remaining 24 million acres are left unused. b. From their original production point, farmers transfer 40 million acres of land from corn to wheat production. They now produce 3.158 billion bushels of wheat and 10.107 bushels of corn. c. Farmers reduce their production of wheat to 2 billion bushels and increase their production of corn to 12.044 billion bushels. Along the production possibility frontier, the opportunity cost of going from 11.807 billion bushels of corn to 12.044 billion bushels of corn is 0.666 bushel of wheat per bushel of corn. 2. a. This point is feasible but not efficient in production. Producing 1.8 billion bushels of wheat and 9 billion bushels of corn is less of both wheat and corn than is possible. They could produce more if all the available farmland were cultivated. b. At this new production point, farmers would now produce 1 billion more bushels of wheat and 1.7 billion fewer bushels of corn than at their original production point. This reflects an opportunity cost of 1.7 bushels of corn per additional bushel of wheat. But, in fact, this new production point is not feasible because we know that opportunity costs are increasing. Starting from the original production point, the opportunity cost of producing 1 more bushel of wheat must be higher than 1.7 bushels of corn. c. This new production point is feasible and efficient in production. Along the production possibility frontier, the economy must forgo 0.666 bushel of wheat per additional bushel of corn. So the increase in corn production from 11.807 billion bushels to 12.044 billion bushels costs the economy (12.044 − 11.807) billion bushels of corn × 0.666 bushel of wheat per bushel of corn = 0.158 bushel of wheat. This is exactly equal to the actual loss in wheat output: the fall from 2.158 billion to 2 billion bushels of wheat. 3. In the ancient country of Roma, only two goods, spaghetti and meatballs, are produced. There are two tribes in Roma, the Tivoli and the Frivoli. By themselves, the Tivoli each month can produce either 30 pounds of spaghetti and no meatballs, or 50 pounds of meatballs and no spaghetti, or any combination in between. The Frivoli, by themselves, each month can produce 40 pounds of spaghetti and no meatballs, or 30 pounds of meatballs and no spaghetti, or any combination in between. a. Assume that all production possibility frontiers are straight lines. Draw one diagram showing the monthly production possibility frontier for the Tivoli and another showing the monthly production possibility frontier for the Frivoli. Show how you calculated them. b. Which tribe has the comparative advantage in spaghetti production? In meatball production? In a.d. 100 the Frivoli discover a new technique for making meatballs that doubles the quantity of meatballs they can produce each month. c. Draw the new monthly production possibility frontier for the Frivoli. d. After the innovation, which tribe now has an absolute advantage in producing meatballs? In producing spaghetti? Which has the comparative advantage in meatball production? In spaghetti production? 3. a. The accompanying diagram shows the production possibility frontier for the Tivoli in panel (a) and for the Frivoli as the line labeled “Original Frivoli PPF” in panel (b). (a) Production possibility frontier for the Tivoli (b) Production possibility frontier for the Frivoli Quantity of spaghetti (pounds) Quantity of spaghetti (pounds) 50 50 40 40 30 30 20 20 10 10 0 10 20 30 40 50 60 Quantity of meatballs (pounds) 0 Original Frivoli PPF New Frivoli PPF 10 20 30 40 50 60 Quantity of meatballs (pounds) The production possibility frontier for the Tivoli was calculated as follows: the Tivoli can produce either 30 pounds of spaghetti and no meatballs, or they can produce no spaghetti but 50 pounds of meatballs. That is, the opportunity cost of 1 pound of meatballs is 3/ 5 of a pound of spaghetti: in order to produce 1 more pound of meatballs, the Tivoli have to give up 3/ 5 of a pound of spaghetti. This means that the slope of their production possibility frontier is − 3/ 5. A similar argument for the Frivoli shows that their production possibility frontier has a slope of − 4/ 3. b. For the Tivoli, the opportunity cost of 1 pound of meatballs is 3/ 5 of a pound of spaghetti. For the Frivoli, the opportunity cost of 1 pound of meatballs is 4/ 3 pounds of spaghetti. That is, the Tivoli have a comparative advantage in meatball production because their opportunity cost is lower. For the Tivoli, the opportunity cost of 1 pound of spaghetti is 5/ 3 pounds of meatballs. For the Frivoli, the opportunity cost of 1 pound of spaghetti is 3/ 4 pound of meatballs. That is, the Frivoli have a comparative advantage in spaghetti production because their opportunity cost is lower. c. The Frivoli’s new production possibility frontier is the line labeled “New Frivoli PPF” in panel (b) of the diagram. Instead of producing 30 pounds of meatballs (if they produce no spaghetti), they can now produce 60 pounds. d. Now the Frivoli have the absolute advantage in both meatball production and spaghetti production. The Frivoli’s opportunity cost of meatballs has now fallen to 4/ 6 = 2/ 3; that is, for each pound of meatballs that the Frivoli now produce, they have to give up producing 2/ 3 of a pound of spaghetti. Since the Frivoli’s opportunity cost of meatballs (2/ 3) is still higher than the Tivoli’s (3/ 5), the Tivoli still have the comparative advantage in meatball production. The Frivoli’s opportunity cost of spaghetti is 3/ 2 pounds of meatballs and the Tivoli’s is 5/ 3 pounds of meatballs, so the Frivoli have the comparative advantage in spaghetti production. 4. One July, the United States sold aircraft worth $1 billion to China and bought aircraft worth only $19,000 from China. During the same month, however, the United States bought $83 million worth of men’s trousers, slacks, and jeans from China but sold only $8,000 worth of trousers, slacks, and jeans to China. Using what you have learned about how trade is determined by comparative advantage, answer the following questions. a. Which country has the comparative advantage in aircraft production? In production of trousers, slacks, and jeans? b. Can you determine which country has the absolute advantage in aircraft production? In production of trousers, slacks, and jeans? 4. a. Since countries gain from specializing in production of the goods and services in which they have a comparative advantage, the United States must have the comparative advantage in aircraft production, and China must have the comparative advantage in production of trousers, slacks, and jeans. b. Since trade has nothing to do with absolute advantage, we cannot determine from these data which country has an absolute advantage in either of these goods. 5. Peter Pundit, an economics reporter, states that the European Union (EU) is increasing its productivity very rapidly in all industries. He claims that this productivity advance is so rapid that output from the EU in these industries will soon exceed that of the United States and, as a result, the United States will no longer benefit from trade with the EU. a. Do you think Peter Pundit is correct or not? If not, what do you think is the source of his mistake? b. If the EU and the United States continue to trade, what do you think will characterize the goods that the EU sells to the United States and the goods that the United States sells to the EU? 5. a. Peter Pundit is not correct. He confuses absolute and comparative advantage. Even if the EU had an absolute advantage over the United States in every product it produced, the United States would still have a comparative advantage in some products. And the United States should continue to produce those products: trade will make both the EU and the United States better off. b. You should expect to see the EU sells those goods in which it has the comparative advantage and the United States sells those goods in which it has the comparative advantage. 6. You are in charge of allocating residents to your dormitory’s baseball and basketball teams. You are down to the last four people, two of whom must be allocated to baseball and two to basketball. The accompanying table gives each person’s batting average and free-throw average. Name Batting average Free-throw average Kelley 70% 60% Jackie 50% 50% Curt 10% 30% Gerry 80% 70% a. Explain how you would use the concept of comparative advantage to allocate the players. Begin by establishing each player’s opportunity cost of free throws in terms of batting average. b. Why is it likely that the other basketball players will be unhappy about this arrangement but the other baseball players will be satisfied? Nonetheless, why would an economist say that this is an efficient way to allocate players for your dormitory’s sports teams? 6. a. Let’s begin by establishing the opportunity cost of free throws for each player. If you allocate Kelley to the basketball team, the team gains a player with a 60% free-throw average and the baseball team loses a player with a 70% batting average. That is, the opportunity cost of allocating Kelley to the basketball team is 7/ 6. Similarly, Jackie’s opportunity cost of playing basketball is 1; Curt’s opportunity cost of playing basketball is 1/ 3, and Gerry’s opportunity cost of playing basketball is 8/ 7. Jackie and Curt have the lowest opportunity costs of playing basketball; that is, they have the comparative advantage in basketball. Therefore, they should be allocated to the basketball team. Kelley and Gerry have the comparative advantage in baseball and should therefore play on the baseball team. b. It is likely that the basketball team will be unhappy with this arrangement. Both Jackie and Curt have an absolute disadvantage at playing basketball, compared to the other two players. (They also have an absolute disadvantage at playing baseball, but they are comparatively less bad at basketball than at baseball.) The baseball team is likely to be happy about this allocation because both Kelley and Gerry have an absolute advantage at playing baseball. However, if you are concerned with the total number of wins for the dormitory (as an economist would be concerned about efficiency), this allocation is the best one: it maximizes the overall chances of the dormitory winning at any sport. 7. The inhabitants of the fictional economy of Atlantis use money in the form of cowry shells. Draw a circular-flow diagram showing households and firms. Firms produce potatoes and fish, and households buy potatoes and fish. Households also provide the land and labor to firms. Identify where in the flows of cowry shells or physical things (goods and services, or resources) each of the following impacts would occur. Describe how this impact spreads around the circle. a. A devastating hurricane floods many of the potato fields. b. A very productive fishing season yields a very large number of fish caught. c. The inhabitants of Atlantis discover Shakira and spend several days a month at dancing festivals. 7. The accompanying diagram illustrates the circular flow for Atlantis. Shells Potatoes and fish Shells Households Land and labor Markets for goods and services Factor markets Potatoes and fish Shells Land and L labor Firms Shells a. The flooding of the fields will destroy the potato crop. Destruction of the potato crop reduces the flow of goods from firms to households: fewer potatoes produced by firms now are sold to households. An implication, of course, is that fewer cowry shells flow from households to firms as payment for the potatoes in the market for goods and services. Since firms now earn fewer shells, they have fewer shells to pay to households in the factor markets. As a result, the amount of factors flowing from households to firms is also reduced. b. The productive fishing season leads to a greater quantity of fish produced by firms to flow to households. An implication is that more money flows from households to firms through the markets for goods and services. As a result, firms want to buy more factors from households (the flow of shells from firms to households increases) and, in return, the flow of factors from households to firms increases. c. Time spent at dancing festivals reduces the flow of labor from households to firms and therefore reduces the number of shells flowing from firms to households through the factor markets. In return, households now have fewer shells to buy goods with (the flow of shells from households to firms in the markets for goods and services is reduced), implying that fewer goods flow from firms to households. 8. An economist might say that colleges and universities “produce” education, using faculty members and students as inputs. According to this line of reasoning, education is then “consumed” by households. Construct a circular-flow diagram to represent the sector of the economy devoted to college education: colleges and universities represent firms, and households both consume education and provide faculty and students to universities. What are the relevant markets in this diagram? What is being bought and sold in each direction? What would happen in the diagram if the government decided to subsidize 50% of all college students’ tuition? 8. The accompanying diagram shows the circular flow for the education sector. Salaries, scholarships Tuition Education Households Faculty, students Academic job market, market for students Education market F Faculty, sstudents Education Tuition Colleges, Universities Salaries, sscholarships Colleges and universities buy faculty on the academic job market and attract students from the market for students. (Many colleges and universities actively try to attract good students by offering scholarships and the like.) They sell education to households in the market for education, and households buy education in that market from one (or sometimes several) of the sellers. If the government subsidized half of all students’ tuition, households would demand more education. As a result, colleges and universities would hire more faculty and accept more students, meaning that more money in terms of salaries and scholarships would flow from universities and colleges to the households. 9. Your dormitory roommate plays loud music most of the time; you, however, would prefer more peace and quiet. You suggest that she buy some headphones. She responds that although she would be happy to use headphones, she has many other things that she would prefer to spend her money on right now. You discuss this situation with a friend who is an economics major. The following exchange takes place: He: How much would it cost to buy headphones? You: $15. He: How much do you value having some peace and quiet for the rest of the semester? You: $30. He: It is efficient for you to buy the headphones and give them to your roommate. You gain more than you lose; the benefit exceeds the cost. You should do that. You: It just isn’t fair that I have to pay for the headphones when I’m not the one making the noise. a. Which parts of this conversation contain positive statements and which parts contain normative statements? b. Construct an argument supporting your viewpoint that your roommate should be the one to change her behavior. Similarly, construct an argument from the viewpoint of your roommate that you should be the one to buy the headphones. If your dormitory has a policy that gives residents the unlimited right to play music, whose argument is likely to win? If your dormitory has a rule that a person must stop playing music whenever a roommate complains, whose argument is likely to win? 9. a. “It is efficient for you to buy the headphones” is a positive statement (it is either right or wrong); that is, it is about description. “You should do that” (that is, buy the headphones) is strictly speaking a normative statement; that is, it is about prescription (although you would find all economists agree that all trades that improve efficiency should be made). “It just isn’t fair” is a normative statement—that is, it is about prescription—and you would likely find much disagreement about the fairness of the proposed trade. b. One argument that your roommate should buy the headphones is that everyone has the right to peace and quiet. If your roommate therefore wants to listen to music, she should have to be responsible for making sure that others’ peace and quiet is not disturbed. Your roommate might argue that since she has the right to play as much music as she wants, it is your responsibility to make sure that you are not disturbed—for instance, by buying her headphones. If the dormitory has a policy that establishes the right to unlimited music, your roommate’s argument wins. If the rule is that there is a right to peace and quiet, your argument wins. 10. A representative of the American clothing industry recently made the following statement: “Workers in Asia often work in sweatshop conditions earning only pennies an hour. American workers are more productive and as a result earn higher wages. In order to preserve the dignity of the American workplace, the government should enact legislation banning imports of low-wage Asian clothing.” a. Which parts of this quote are positive statements? Which parts are normative statements? b. Is the policy that is being advocated consistent with the preceding statements about the wages and productivities of American and Asian workers? c. Would such a policy make some Americans better off without making any other Americans worse off? That is, would this policy be efficient from the viewpoint of all Americans? d. Would low-wage Asian workers benefit from or be hurt by such a policy? 10. a. The positive statements are: ■ workers in Asia . . . [are] earning only pennies an hour ■ American workers are more productive ■ American workers are more productive and as a result earn higher wages The normative statement is: ■ the government should enact legislation banning imports of low-wage Asian clothing b. It is not. The statement about the productivity of American and Asian workers is about the absolute advantage that American workers have over Asian workers. However, Asian workers may still have a comparative advantage. And if that is the case, then banning imports would result in inefficiency. c. If America channeled more of its productive resources into producing clothing, it would have to give up producing other goods. As a result, America would be able to consume less of all goods. And this would make some A mericans clearly worse off. Therefore, this policy would not be efficient. d. Low-wage Asian workers would also be hurt by this policy. The Asian country would channel its resources away from producing clothing toward producing other goods that it previously imported from America. But since it does not have the comparative advantage in those other goods, the Asian country would be able to consume less of all goods. 11. Are the following statements true or false? Explain your answers. a. “When people must pay higher taxes on their wage earnings, it reduces their incentive to work” is a positive statement. b. “We should lower taxes to encourage more work” is a positive statement. c. Economics cannot always be used to completely decide what society ought to do. d. “The system of public education in this country generates greater benefits to society than the cost of running the system” is a normative statement. e. All disagreements among economists are generated by the media. 11. a. True. This is a positive statement. It has a factual answer; that is, it is either right or wrong. There has been some debate about whether the statement is actually true or false, but in principle there is only one answer. b. False. This is a statement about what we should do, and this statement has no clearly right or wrong answer. Your view will depend on whether you think encouraging more work is a good or a bad idea. c. True. Economics is best at giving positive answers, for instance, answers about what the most efficient way is of achieving a certain aim. The question of how society ought to be organized is mostly decided in the realm of politics. d. False. This is a positive statement. In principle, it has an answer that is either right or wrong. e. False. Some disagreements among economists arise from the fact that in building a model, one economist thinks that a certain abstraction from reality is admissible but another economist may think that that abstraction is not admissible. Some disagreements arise from the fact that economists sometimes disagree about values. 12. Evaluate the following statement: “It is easier to build an economic model that accurately reflects events that have already occurred than to build an economic model to forecast future events.” Do you think this is true or not? Why? What does this imply about the difficulties of building good economic models? 12. True. With hindsight it is easier to see the important features of the situation that a model should have captured. For predictive purposes, a model needs to anticipate which features of reality are important (and so should be included) and which are unimportant (and so can be ignored). This is why the famed British economist John Maynard Keynes referred to economics as an art as well as a science. 13. Economists who work for the government are often called on to make policy recommendations. Why do you think it is important for the public to be able to differentiate normative statements from positive statements in these recommendations? 13. Positive statements are those based on fact—or at least on our best estimate of what the facts are. Therefore, these statements are also those that do not depend on the political views of the economist. Normative statements may sometimes be influenced by the economist’s own values. Whether someone agrees with an economist’s normative statement may depend on whether they share values. It is therefore important that the public be able to distinguish normative from positive statements. 14. The mayor of Gotham City, worried about a potential epidemic of deadly influenza this winter, asks an economic adviser the following series of questions. Determine whether a question requires the economic adviser to make a positive assessment or a normative assessment. a. How much vaccine will be in stock in the city by the end of November? b. If we offer to pay 10% more per dose to the pharmaceutical companies providing the vaccines, will they provide additional doses? c. If there is a shortage of vaccine in the city, whom should we vaccinate first—the elderly or the very young? (Assume that a person from one group has an equal likelihood of dying from influenza as a person from the other group.) d. If the city charges $25 per shot, how many people will pay? e. If the city charges $25 per shot, it will make a profit of $10 per shot, money that can go to pay for inoculating poor people. Should the city engage in such a scheme? 14. a. Positive b. Positive c. Normative d. Positive e. Normative 15. Assess the accuracy of the following statement: “If economists just had enough data, they could solve all policy questions in a way that maximizes the social good. There would be no need for divisive political debates, such as whether the government should provide free medical care for all.” Frame your answer using the concepts of positive and normative economics. 15. What is true is that if economists had enough data, they could predict precisely what the outcome would be of any proposed policy (such as free medical care). That is, economists can answer positive questions. But no amount of data can lead to a determination about what a society should do—that is a normative question. An economist can predict how much it will cost to provide free medical care and what effects different ways of raising taxes will have on people’s behavior (for instance, a sales tax will reduce consumption behavior; an income tax may discourage workers from working as much as before). But whether this is a trade-off worth making is a question that can be answered only in political discourse. WORK IT OUT Interactive step-by-step help with solving this problem can be found online. 16. Atlantis is a small, isolated island in the South Atlantic. The inhabitants grow potatoes and catch fish. The accompanying table shows the maximum annual output combinations of potatoes and fish that can be produced. Obviously, given their limited resources and available technology, as they use more of their resources for potato production, there are fewer resources available for catching fish. Maximum annual output options Quantity of potatoes (pounds) Quantity of fish (pounds) A B C D E F 1,000 800 600 400 200 0 0 300 500 600 650 675 a. Draw a production possibility frontier with potatoes on the horizontal axis and fish on the vertical axis illustrating these options, showing points A–F. b. Can Atlantis produce 500 pounds of fish and 800 pounds of potatoes? Explain. Where would this point lie relative to the production possibility frontier? c. What is the opportunity cost of increasing the annual output of potatoes from 600 to 800 pounds? d. What is the opportunity cost of increasing the annual output of potatoes from 200 to 400 pounds? e. Can you explain why the answers to parts c and d are not the same? What does this imply about the slope of the production possibility frontier? 16. a. The accompanying diagram shows the production possibility frontier for Atlantis. Quantity of fish (pounds) 675 650 600 F E D C 500 G B 300 Atlantis PPF A 0 200 400 600 800 1,000 Quantity of potatoes (pounds) b. No, Atlantis cannot produce 500 pounds of fish and 800 pounds of p otatoes. If it produces 500 pounds of fish, the most potatoes it can produce is 600 pounds. This point would lie outside the production possibility frontier, at point G on the diagram. c. The opportunity cost of increasing output from 600 to 800 pounds of potatoes is 200 pounds of fish. If Atlantis increases output from 600 to 800 pounds of potatoes, it has to cut fish production from 500 pounds to 300 pounds, that is, by 200 pounds. d. The opportunity cost of increasing output from 200 to 400 pounds of potatoes is 50 pounds of fish. If Atlantis increases output from 200 to 400 pounds of potatoes, it has to cut fish production from 650 pounds to 600 pounds, that is, by 50 pounds. e. The answers to parts c and d imply that the more potatoes Atlantis produces, the higher the opportunity cost becomes. For instance, as you grow more and more potatoes, you have to use less and less suitable land to do so. As a result, you have to divert increasingly more resources away from fishing as you grow more potatoes, meaning that you can produce increasingly less fish. This implies, of course, that the production possibility frontier becomes steeper the farther you move along it to the right; that is, the production possibility frontier is bowed out. (Mathematicians call this shape concave.) Graphs in Economics 1. Study the four accompanying diagrams. Consider the following statements and indicate which diagram matches each statement. Which variable would appear on the horizontal and which on the vertical axis? In each of these statements, is the slope positive, negative, zero, or infinity? Panel (a) Panel (b) Panel (c) Panel (d) a. If the price of movies increases, fewer consumers go to see movies. b. More experienced workers typically have higher incomes than less experienced workers. c. Whatever the temperature outside, Americans consume the same number of hot dogs per day. d. Consumers buy more frozen yogurt when the price of ice cream goes up. e. Research finds no relationship between the number of diet books purchased and the number of pounds lost by the average dieter. f. Regardless of its price, Americans buy the same quantity of salt. 1. a. Panel (a) illustrates this relationship. The higher price of movies causes consumers to see fewer movies. The relationship is negative, and the slope is therefore negative. The price of movies is the independent variable, and the number of movies seen is the dependent variable. However, there is a convention in economics that if price is a variable, it is measured on the vertical axis. So the quantity of movies is measured on the horizontal axis. b. Panel (c) illustrates this relationship. Since it is likely that their greater experience causes firms to pay workers more, years of experience is the independent variable and would go on the horizontal axis and the resulting income, the dependent variable, on the vertical axis. The slope is positive. c. Panel (d) illustrates this relationship. With the temperature on the horizontal axis as the independent variable, and the consumption of hot dogs on the vertical axis as the dependent variable, we see there is no change in hot dog consumption whatever the temperature. The slope is zero. 2 Appendix d. Panel (c) illustrates this relationship. When the price of ice cream goes up, this causes consumers to choose a close alternative, frozen yogurt. The price of ice cream is the independent variable and the consumption of frozen yogurt is the dependent variable. However, there is a convention in economics that if price is a variable, it is measured on the vertical axis. The quantity of frozen yogurt that consumers buy is on the horizontal axis. The slope is positive. e. Panel (d) illustrates this relationship. The fact that there is no discernible relationship between the number of diet books purchased and the weight loss of the average dieter results in a horizontal curve. The slope is zero. f. Panel (b) illustrates this relationship. Although price is the independent variable and salt consumption the dependent variable, by convention the price appears on the vertical axis and the quantity of salt on the horizontal axis. Since salt consumption does not change whatever the price, the curve is a vertical line; the slope is infinity. 2. During the Reagan administration, economist Arthur Laffer argued in favor of lowering income tax rates in order to increase tax revenues. Like most economists, he believed that at tax rates above a certain level, tax revenue would fall because high taxes would discourage some people from working and that people would refuse to work at all if they received no income after paying taxes. This relationship between tax rates and tax revenue is graphically summarized in what is widely known as the Laffer curve. Plot the Laffer curve relationship assuming that it has the shape of a nonlinear curve. The following questions will help you construct the graph. a. Which is the independent variable? Which is the dependent variable? On which axis do you therefore measure the income tax rate? On which axis do you measure income tax revenue? b. What would tax revenue be at a 0% income tax rate? c. The maximum possible income tax rate is 100%. What would tax revenue be at a 100% income tax rate? d. Estimates now show that the maximum point on the Laffer curve is (approximately) at a tax rate of 80%. For tax rates less than 80%, how would you describe the relationship between the tax rate and tax revenue, and how is this relationship reflected in the slope? For tax rates higher than 80%, how would you describe the relationship between the tax rate and tax revenue, and how is this relationship reflected in the slope? 2. a. The income tax rate is the independent variable and so is measured on the horizontal axis. Income tax revenue is the dependent variable and so is measured on the vertical axis. Income tax revenue 0 80 100% Income tax rate (percent) b. If the income tax rate is 0% (there is no tax), tax revenue is obviously zero. c. If the income tax rate is 100% (all your income is taxed away), you will have zero income left after tax. Since people are unwilling to work if they receive no income after tax, no income will be earned. As a result, there is no income tax revenue. d. For tax rates less than 80%, tax rate and tax revenue are positively related and so the Laffer curve has a positive slope. For tax rates higher than 80%, the relationship between tax rate and tax revenue is negative and so the Laffer curve has a negative slope. The Laffer curve therefore looks like the accompanying diagram with a maximum point at a tax rate of 80%. 3. In the accompanying figures, the numbers on the axes have been lost. All you know is that the units shown on the vertical axis are the same as the units on the horizontal axis. y Panel (a) y x Panel (b) x a. In panel (a), what is the slope of the line? Show that the slope is constant along the line. b. In panel (b), what is the slope of the line? Show that the slope is constant along the line. 3. a. In panel (a), the slope is -2. From any point on the line, moving one unit to the right along the horizontal axis requires moving down two units along the vertical axis in order to remain on the line. The slope is the rise (-2) over the run (+1); that is, the slope is -2 1 = -2. The same is true starting at any point along the line, so the slope at every point is the same. The slope is constant. b. In panel (b), the slope is 1 . 3 From any point on the line, moving three units to the right along the horizontal axis requires moving up one unit along the vertical axis in order to remain on the line. The slope is the rise (+1) over the run (+3); that is, the slope is 1 . 3 The same is true starting at any point along the line, so the slope at every point is the same. The slope is constant. 4. Answer each of the following questions by drawing a schematic diagram. a. Taking measurements of the slope of a curve at three points farther and farther to the right along the horizontal axis, the slope of the curve changes from -0.3, to -0.8, to -2.5, measured by the point method. Draw a schematic diagram of this curve. How would you describe the relationship illustrated in your diagram? b. Taking measurements of the slope of a curve at five points farther and farther to the right along the horizontal axis, the slope of the curve changes from 1.5, to 0.5, to 0, to -0.5, to -1.5, measured by the point method. Draw a schematic diagram of this curve. Does it have a maximum or a minimum? 4. a. The accompanying diagram schematically shows this curve. The slope is negative throughout. That means that the curve is downward sloping. Because the absolute value of the slope is increasing, the curve becomes steeper. The slope is negative increasing. y Slope = –0.3 Slope = –0.8 Slope = –2.5 x b. The accompanying diagram schematically shows this curve. The slope is positive decreasing at first. Then it becomes negative increasing. The curve therefore has a maximum just at the point where the slope is equal to zero. y Slope = 0 Slope = 0.5 Slope = 1.5 Slope = –0.5 Slope = –1.5 x 5. For each of the accompanying diagrams, calculate the area of the shaded right triangle. Panel (a) y 5 100 4 80 3 60 2 40 1 20 0 1 2 3 4 x 10 40 8 30 6 20 4 10 2 10 20 30 40 50 x 10 15 20 25 x 4 5 Panel (d) y 50 0 5 0 Panel (c) y Panel (b) y 0 1 2 3 x 5. a. In panel (a), the height of the shaded triangle is 5 − 0 = 5, and its base is 4 − 0 = 4. The area of the triangle is 5×4 2 = 10. b. In panel (b), the height of the shaded triangle is 100 − 60 = 40, and its base is 10 − 0 = 10. The area of the triangle is 40 × 10 2 = 200. 20 × 40 2 = 400. c. In panel (c), the height of the shaded triangle is 40 − 20 = 20, and its base is 40 - 0 = 40. The area of the triangle is d. In panel (d), the height of the shaded triangle is 8 − 0 = 8, and its base is 4 − 0 = 4. The area of the triangle is 8×4 2 = 16. 6. The base of a right triangle is 10, and its area is 20. What is the height of this right triangle? 6. The area of a right triangle is calculated as Height × Base = Area 2 Substituting what we know from the question (base = 10 and area = 20), we get Height × 10 = 20 2 Solving this for height, we find that the height of this right triangle is 4. 7. The accompanying table shows the relationship between workers’ hours of work per week and their hourly wage rate. Apart from the fact that they receive a different hourly wage rate and work different hours, these five workers are otherwise identical. Name Quantity of labor (hours per week) Wage rate (per hour) Athena 30 $15 Boris 35 30 Curt 37 45 Diego 36 60 Emily 32 75 a. Which variable is the independent variable? Which is the dependent variable? b. Draw a scatter diagram illustrating this relationship. Draw a (nonlinear) curve that connects the points. Put the hourly wage rate on the vertical axis. c. As the wage rate increases from $15 to $30, how does the number of hours worked respond according to the relationship depicted here? What is the average slope of the curve between Athena’s and Boris’s data points using the arc method? d. As the wage rate increases from $60 to $75, how does the number of hours worked respond according to the relationship depicted here? What is the average slope of the curve between Diego’s and Emily’s data points using the arc method? 7. a. If the wage rate is greater than your opportunity cost of time, you will choose to work. So the wage rate is the independent variable and the number of hours worked is the dependent variable. b. The accompanying diagram illustrates the relationship between the hourly wage rate and the number of hours worked. Since the hourly wage rate is the price paid for labor, economists place wages on the vertical axis—just as in the case of other types of prices. Wage rate (per hour) $75 60 45 30 15 0 28 29 30 31 32 33 34 35 36 37 Quantity of labor (hours per week) c. As the wage rate increases from $15 to $30, the number of hours worked increases by 5. The average slope of the curve between the two points is therefore 15 5 = 3. d. As the wage rate increases from $60 to $75, the number of hours worked decreases by 4. The average slope of the curve between the two points is therefore 15 -4 = -3.75. 8. An insurance company has found that the severity of property damage in a fire is positively related to the number of firefighters arriving at the scene. a. Draw a diagram that depicts this finding with number of firefighters on the horizontal axis and amount of property damage on the vertical axis. What is the argument made by this diagram? Suppose you reverse what is measured on the two axes. What is the argument made then? b. Should the insurance company ask the city to send fewer firefighters to any fire in order to reduce its payouts to policy holders? 8. a. By drawing the diagram with number of firefighters on the horizontal axis and amount of property damage on the vertical axis, you are assuming that the number of firefighters is the independent variable and amount of property damage is the dependent variable. That graph is shown here. It makes the argument that as the number of firefighters on the scene increases, the amount of damage increases. You could also have drawn the graph with amount of property damage as the independent variable (on the horizontal axis) and the number of firefighters as the dependent variable (on the vertical axis). In this case the diagram implies that more and more firefighters come to the scene as the amount of property damage increases. (But be aware that any diagram shows only a relationship between two variables and does not imply causation.) Amount of property damage Number of firefighters b. The statement implies that there is a causal link between the number of firefighters and the amount of property damage, and this is likely not the case. It is instead likely that there is a third, omitted, variable that is related to both the number of firefighters and the amount of property damage. This variable is the severity of the fire: more severe fires cause both greater property damage and a greater number of firefighters to be sent to the fire. 9. This table illustrates annual salaries and income tax owed by five individuals. Despite receiving different annual salaries and owing different amounts of income tax, these five individuals are otherwise identical. Name Annual salary Annual income tax owed Susan $22,000 $3,304 63,000 14,317 3,000 454 Camila 94,000 23,927 Peter 37,000 7,020 Eduardo John a. If you were to plot these points on a graph, what would be the average slope of the curve between the points for Eduardo’s and Camila’s salaries and taxes using the arc method? How would you interpret this value for slope? b. What is the average slope of the curve between the points for John’s and Susan’s salaries and taxes using the arc method? How would you interpret that value for slope? c. What happens to the slope as salary increases? What does this relationship imply about how the level of income taxes affects a person’s incentive to earn a higher salary? 9. a. Annual salary is the independent variable and so is measured on the horizontal axis. Annual income tax owed is the dependent variable and so is measured on the vertical axis. As salary increases by $31,000 from Eduardo’s $63,000 to Camila’s $94,000, income tax owed increases by $9,610. That is, the slope of the curve is 9,610 31,000 = 0.31. The interpretation is that in this income bracket, each additional dollar of income implies a tax of $0.31. b. As salary increases by $19,000 from John’s $3,000 to Susan’s $22,000, income tax owed increases by $2,850. That is, the slope of the curve is 2,850 19,000 = 0.15. The interpretation is that in this income bracket, each additional dollar of income implies a tax of $0.15. c. The slope is positive increasing. This implies that the tax scheme is “progressive”: the higher the annual salary, the greater the amount of income tax owed per dollar of income. Therefore, the incentive to earn more and more income becomes weaker and weaker, since more of the additional income earned is owed as income taxes. WORK IT OUT Interactive step-by-step help with solving this problem can be found online. 10. Studies have found a relationship between a country’s yearly rate of economic growth and the yearly rate of increase in airborne pollutants. It is believed that a higher rate of economic growth allows a country’s residents to have more cars and travel more, thereby releasing more airborne pollutants. a. Which variable is the independent variable? Which is the dependent variable? b. Suppose that in the country of Sudland, when the yearly rate of economic growth fell from 3.0% to 1.5%, the yearly rate of increase in airborne pollutants fell from 6% to 5%. What is the average slope of a nonlinear curve between these points using the arc method? c. Assume that when the yearly rate of economic growth rose from 3.5% to 4.5%, the yearly rate of increase in airborne pollutants rose from 5.5% to 7.5%. What is the average slope of a nonlinear curve between these two points using the arc method? d. How would you describe the relationship between the two variables here? 10. a. According to the question, economic growth causes the increase in airborne pollutants. That is, the growth rate is the independent variable and the rate of increase in airborne pollutants is the dependent variable. So the rate of increase in airborne pollutants is measured on the vertical axis and the growth rate is measured on the horizontal axis. b. The change in the growth rate is −1.5. The change in the rate of increase in airborne pollutants is −1. The slope is therefore -1 -1.5 = 2 . 3 c. The change in the growth rate is +1. The change in the rate of increase in airborne pollutants is +2. The slope is therefore 2 1 = 2. d. The slope is positive and, as can be seen from the answers to parts b and c, increasing. Solution Manual for Microeconomics Paul Krugman, Robin Wells 9781319098780
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