# use of mathematics in economics

Or put into other words, mathematics such as calculus, matrix algebra, and differential equations are applied to illustrate economic theories and analyze economic hypotheses. Information, Risk, and Insurance, Introduction to Information, Risk, and Insurance, 16.1 The Problem of Imperfect Information and Asymmetric Information, 17.1 How Businesses Raise Financial Capital, 17.2 How Households Supply Financial Capital, 18.1 Voter Participation and Costs of Elections, 18.3 Flaws in the Democratic System of Government, Chapter 19. Joan Robinson (1956) was engaged in academic politics when she waged her campaign against capital and the aggregate production function. Answer (1 of 3): Mathematics is vital to economics as it allows clarity when issues are being discussed. For example (using words), your professor is Adam Smith. So if you find some math in the book that you cannot follow, come back to this appendix to review. Answering specific questions requires solving the “system” of equations that represent the model. Any graph is a single visual perspective on a subject. Economics is not math. Note that you cannot do anything about your SAT score, since if you are in college, you have (presumably) already taken the SATs. Figure 4 presents another example of a line graph, representing the data from Table 3. The b term is called the y-intercept. For example, suppose your GPA was determined as follows: This equation states that your GPA depends on three things: your combined SAT score, your class attendance, and the number of hours you spend studying. Now imagine you wanted to emphasize how unemployment spiked substantially higher in 2009. b y running on-line auctions to purchase. Thus, a time series graph shows how a variable changes over time. Math is one way of working with (or manipulating) economic models. A positive slope means that two variables are positively related; that is, when x increases, so does y, or when x decreases, y decreases also. As some have noted, Coase (1937, 1960, etc.) By spreading the graph wide and flat, the visual appearance is that the rise in unemployment is not so large, and is similar to some past rises in unemployment. Pie graphs are often better than line graphs at showing how an overall group is divided. The data in Table 2 is displayed in Figure 3 which shows the relationship between two variables: length and median weight for American baby boys and girls during the first three years of life. Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets.Generally, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. The slices of this circular “pie” show the relative sizes of subgroups. Since P is on the vertical axis, it is easiest if you solve each equation for P. The demand curve is then P = 8 – 0.5Qd and the demand curve is P = –0.4 + 0.2Qs. It also says that study time is twice as important (0.50) as either combined_SAT score (0.25) or class_attendance (0.25). The market for mathematical theory can sur-vive a few lemon articles ﬁlled with mathiness. Air density is measured by the weight of the air in a cubic meter of space (that is, a box measuring one meter in height, width, and depth). Suppose the slope of a line were to increase. Robert Solow (1956) was engaged in science when he developed his mathematical theory of growth. A graph is just one perspective or point of view, shaped by choices such as those discussed in this section. Your boss, however, is so impressed with your work that he gives you a \$2 per hour raise. This kind of graph is widely used by healthcare providers to check whether a child’s physical development is roughly on track. It also says that study time is twice as important (0.50) as either combined\_SAT score (0.25) or class\_attendance (0.25). You can also download for free at http://cnx.org/contents/[email protected], Length to Weight Relationship for American Boys and Girls, U.S. Age Distribution, 1970, 2000, and 2030 (projected), Leading 12 Countries of the World by Population, Creative Commons Attribution 4.0 International License, http://cnx.org/contents/[email protected], How to interpret the equation of a line (i.e., slope and intercept), How to manipulate a line (i.e., changing the slope or the intercept), How to compute and interpret a growth rate (i.e., percentage change), For questions regarding this license, please contact. "Download for free at, If you redistribute part of this textbook, then you must retain in every digital format page view (including but not limited to EPUB, PDF, and HTML) and on every physical printed page the following attribution: Graph of linear demand function is shown in Figure 5.1. Compared to Figure 5, where the vertical scale runs from 0% to 12%, Figure 10 (c) makes the fluctuation in unemployment look smaller, while Figure 10 (d) makes it look larger. Of course, economic models express relationships using economic variables, like Budget = money_spent_on_econ_books + money_spent_on_music, assuming that the only things you buy are economics books and music. Economics is not math. A negative slope means that two variables are negatively related; that is, when x increases, y decreases, or when x decreases, y increases. The variable on the left-hand side is what is being explained (“the effect”). Not all relationships in economics are linear. In a pie chart with many small slices and one large slice, someone must decided what categories should be used to produce these slices in the first place, thus making some slices appear bigger than others. You can, however, get a good intuitive sense of these 600 data points very quickly from the graph. The length-weight relationship and the altitude-air density relationships in these two figures represent averages. The reason for this name is that, if x = 0, then the b term will reveal where the line intercepts, or crosses, the y-axis. Why is a bar chart the best way to illustrate comparisons? If you draw the graphs carefully, you will see that where they cross (Qs = Qd), the price is \$2 and the quantity is 12, just like the algebra predicted. A growth rate is simply the percentage change in some quantity. To calculate slope, begin by designating one point as the “starting point” and the other point as the “end point” and then calculating the rise over run between these two points. Mathematics are necessary for economics for two big reasons: clarity of argument and quantitative prediction. By averaging out some of the year- to-year changes, the line appears smoother and with fewer highs and lows. [link] shows that a cubic meter of air at an altitude of 500 meters weighs approximately one kilogram (about 2.2 pounds). The relationship between mathematics and economics is essential and some applications of mathematics in relation to economics include: • Statistical analysis This is vital to the running of any business, and is an important part of any business plan. In the figure, these points are plotted and a line is drawn through them. Perhaps the real issue is not the difficulty but the "proper" use of maths in this field. A little math ability goes a long way; the more advanced math you bring in, the less additional knowledge that will get you. Statistics is the area of mathematics we use to explore and try to explain the uncertain world in which we live. Suppose a line has a larger intercept. I’ve been getting some comments from people who think my magazine piece was an attack on the use of mathematics in economics. Although there are some studies tackling these issues, those use either a little amount of papers, a small amount of scholars or cover a short period of time. Math is one way of working with (or manipulating) economic models. Similarly, in measuring the height and weight of children for the previous line graph, children of a particular height would have a range of different weights, some above average and some below. It is an indispensable tool for an economist to understand various business and economic problems and formulate policies to tackle with them. In this case, the line graph shows how thin the air becomes when you climb a mountain. Suppose the demand for personal pizzas is given by the following equation: where Qd is the amount of personal pizzas consumers want to buy (i.e., quantity demanded), and P is the price of pizzas. We will use graphs more frequently in this book than algebra, but now you know the math behind the graphs. Of course, economic models express relationships using economic variables, like Budget = money\_spent\_on\_econ\_books + money\_spent\_on\_music, assuming that the only things you buy are economics books and music. In particular, Puu discusses the contents of the typical treatises (written untill the mid 20th Century), which reflect the totality of applications of mathematics to economics by Advanced courses cover areas including statistics, econometric theory, and productivity and efficiency analysis. The three pie graphs in [link] show that the share of the U.S. population 65 and over is growing. The slices of this circular “pie” show the relative sizes of subgroups. That is, mathematics is used to “solve” the model. You'll learn about the methods economists use to measure, analyse, predict and model a broad range of economic scenarios. You can get away with fuzzy thinking in your head, but you cannot when you reduce a model to algebraic equations. Mathematical economics is best defined as a sub-field of economics that examines the mathematical aspects of economics and economic theories. … The algebraic equation for a line is y = b + mx, where x is the variable on the horizontal axis and y is the variable on the vertical axis, the b term is the y-intercept and the m term is the slope. However, as the altitude increases, air density decreases. It could be a business’s sales. Although you may know that China and India are the most populous countries in the world, seeing how the bars on the graph tower over the other countries helps illustrate the magnitude of the difference between the sizes of national populations. The m term in the equation for the line is the slope. Bar graphs can also compare size, quantity, rates, distances, and other quantitative categories. Economists use models as the primary tool to derive insights about economic issues and problems. The three pie graphs in Figure 6 show that the share of the U.S. population 65 and over is growing. A smaller growth rate means the quantity is growing more slowly. Or Friends = Bob + Shawn + Margaret. Figure 8 (a) shows three bars for each year, representing the total number of persons in each age bracket for each year. The Impacts of Government Borrowing, Introduction to the Impacts of Government Borrowing, 31.1 How Government Borrowing Affects Investment and the Trade Balance, 31.2 Fiscal Policy, Investment, and Economic Growth, 31.3 How Government Borrowing Affects Private Saving, Chapter 32. Sometimes it is useful to show more than one set of data on the same axes. In the third year, the same \$2 raise would correspond to a \$2/\$14 = 14.2%. Economists mostly stick to science. Thus, the slope of a straight line between these two points would be that from the altitude of 4,000 meters up to 6,000 meters, the density of the air decreases by approximately 0 The altitude-air density relationship, shown in [link] later in this appendix, has a negative slope. Remember the saying a picture is worth a thousand words? Math helps economists solve concrete problems involving numbers, such as how to calculate the profit margin of a firm, what price a company should set to maximize profits, or how to calculate the amount of CO2 emissions in the atmosphere. For example, which countries have larger or smaller populations? The percentage change (or growth rate) in your pay is \$2/\$10 = 0.20 or 20%. Types of Math. Suppose the slope of a line were to decrease. The graphs we have discussed so far are called line graphs, because they show a relationship between two variables: one measured on the horizontal axis and the other measured on the vertical axis. In a pie chart with many small slices and one large slice, someone must decided what categories should be used to produce these slices in the first place, thus making some slices appear bigger than others. The impression it leaves will be based on many choices, such as what data or time frame is included, how data or groups are divided up, the relative size of vertical and horizontal axes, whether the scale used on a vertical starts at zero. This is fine for a one-time calculation, but when we compute the growth over and over, it makes more sense to define the quantity as the average quantity over the period in question, which is defined as the quantity halfway between the initial quantity and the next quantity. The graph includes monthly data since 1960, which over almost 50 years, works out to nearly 600 data points. The graphs we have discussed so far are called line graphs, because they show a relationship between two variables: one measured on the horizontal axis and the other measured on the vertical axis. It is the same thing. A function describes a relationship. By not skipping class and studying more. Economic models can be solv… To a mathematician or an economist, a variable is the name given to a quantity that may assume a range of values. There is no important concept in this course that cannot be explained without mathematics. Economic models can be solved algebraically or graphically. A vertical line has an infinite slope. I should know! Figure 11 (g), however, shows a graph that goes back only to 1975, which gives an impression that unemployment was more-or-less gradually falling over time until the 2009 recession pushed it back up to its “original” level—which is a plausible interpretation if one starts at the high point around 1975. Math in economics can be extremely useful. The altitude-air density relationship, shown in Figure 4 later in this appendix, has a negative slope. Some common examples of how pie graphs are used include dividing the population into groups by age, income level, ethnicity, religion, occupation; dividing different firms into categories by size, industry, number of employees; and dividing up government spending or taxes into its main categories. Suppose the slope of a line were to increase. A negative growth rate means the quantity is decreasing. Graphically, that means it would shift out (or up) from the old origin, parallel to the old line. Macroeconomic Policy Around the World, Introduction to Macroeconomic Policy around the World, 32.1 The Diversity of Countries and Economies across the World, 32.2 Improving Countries’ Standards of Living, 32.3 Causes of Unemployment around the World, 32.4 Causes of Inflation in Various Countries and Regions, 33.2 What Happens When a Country Has an Absolute Advantage in All Goods, 33.3 Intra-industry Trade between Similar Economies, 33.4 The Benefits of Reducing Barriers to International Trade, Chapter 34. One line on the graph shows the length-weight relationship for boys and the other line shows the relationship for girls. The slope of a line is the same at any point on the line and it indicates the relationship (positive, negative, or zero) between two economic variables. A higher positive slope means a steeper upward tilt to the line, while a smaller positive slope means a flatter upward tilt to the line. We will use graphs more frequently in this book than algebra, but now you know the math behind the graphs. The slope of a straight line between two points can be calculated in numerical terms. There is a widespread public misconception about the level of difficulty of mathematics used by economists. This kind of graph is widely used by healthcare providers to check whether a child’s physical development is roughly on track. Mathematics comes hand in hand with economics. In recent years, teaching mathematics to economics students has become increasingly challenging for universities across the sector, regardless of entry qualifications. The course is one of the most important in the whole programme, since it provides a systematic overview of mathematical methods used in economics. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises. These graphs all illustrate the unemployment rate—but from different perspectives. That said, math is a tool that can be used to illustrate economic concepts. MATHEMATICS MEANING HISTORY and USE IN REAL LIFE In HINDI - Duration: 6:14. We will learn in other chapters that price and quantity supplied have a positive relationship; that is, firms will supply more when the price is higher. A negative slope that is larger in absolute value (that is, more negative) means a steeper downward tilt to the line. Graphically, that means it would get steeper. A similar effect can be accomplished without changing the length of the axes, but by changing the scale on the vertical axis. A bar graph uses the height of different bars to compare quantities. If you are making a bar graph, you can make the vertical axis either taller or shorter, which will tend to make variations in the height of the bars appear more or less. Skip to main content.ca Hello, Sign in. The pie graphs allow you to get a feel for the relative size of the different age groups from 1970 to 2000 to 2030, without requiring you to slog through the specific numbers and percentages in the table. Economics is not math. A cubic meter of air at the top of Mount Everest, at about 8,828 meters, would weigh only 0.023 kilograms. update 1 . Debunking the use of mathematics in economics 28 May, 2015 at 20:02 | Posted ... he became an economist, used to say that when he met wordy mathematical expositions,that he usually read only the text that accompanied them to see if the author could have something relevant to say, and if it could be true. Comparing Line Graphs with Pie Charts and Bar Graphs. The data in [link] is displayed in [link] which shows the relationship between two variables: length and median weight for American baby boys and girls during the first three years of life. It disciplines your thinking by making you specify exactly what you mean. (This appendix should be consulted after first reading Welcome to Economics!) The line graph measures length in inches on the horizontal axis and weight in pounds on the vertical axis. As the graph shows, air pressure is heaviest at ground level and becomes lighter as you climb. Three types of graphs are used in this book: line graphs, pie graphs, and bar graphs. For example, 50% would be half of the pie and 20% would be one-fifth of the pie. Growth rates are frequently encountered in real world economics. For example, it is important to know the rate at which quantity demanded of a commodity changes in response to a change in price of a commodity. It will be worth your while in terms of helping you learn advanced economics more quickly. Economists often use models to answer a specific question, like: What will the unemployment rate be if the economy grows at 3% per year? Graphs are also used to display data or evidence. But in the second year, the growth rate would be \$2/\$12 = 0.167 or 16.7% growth. In general, I think you would be hard-pressed to find many fields of mathematics that have been successfully used in physics but never used in economics or econometrics or mathematical finance in one way or another. Most of my own work over the years has relied on sometimes finicky math — I spent quite a few years of my life doing tricks with constant-elasticity-of-substitution Reading that list of 600 data points in numerical form would be hypnotic. This means we did our math correctly, since Qd = Qs. Instead of a picture, think of a graph. This could be expressed as Professor = Adam Smith. Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Economic models can be solved algebraically or graphically. The Mathematics in Business and Economics program at the University of Mannheim teaches us to use our mathematical knowledge to solve problems from the business world. Remember that slope is defined as rise over run; more specifically, the slope of a line from one point to another is the change in the vertical axis divided by the change in the horizontal axis. The reason why economists adopted mathematics as the language (and yes it is a language!) But why would you use your fist to bang a nail, if you had a hammer? The subject matter of economics is social behavior. If you need a rough approximation, use the first method. Another way to alter the perception of the graph is to reduce the amount of variation by changing the number of points plotted on the graph. If you got a \$2 raise each year, in the first year the growth rate would be \$2/\$10 = 20%, as shown above. The points for the unemployment rate in each year are plotted on the graph, and a line then connects the points, showing how the unemployment rate has moved up and down since 1975. A circle represents a group as a whole. A positive slope means that two variables are positively related; that is, when x increases, so does y, or when x decreases, y decreases also. The points for the unemployment rate in each year are plotted on the graph, and a line then connects the points, showing how the unemployment rate has moved up and down since 1975. We consider three 'cases studies' of the uses and mis-uses of mathematics in economics and econometrics. Environmental Protection and Negative Externalities, Introduction to Environmental Protection and Negative Externalities, 12.4 The Benefits and Costs of U.S. Environmental Laws, 12.6 The Tradeoff between Economic Output and Environmental Protection, Chapter 13. Thus, any graph should be regarded somewhat skeptically, remembering that the underlying relationship can be open to different interpretations. The study of statistics, especially when combined with computer statistics and spreadsheet programs, is a great help in organizing this kind of data, plotting line graphs, and looking for typical underlying relationships. Second Edition Published in July 2014 . However, if a pie graph has too many slices, it can become difficult to interpret. The horizontal axis of the figure shows altitude, measured in meters above sea level. What do the slices of a pie chart represent? A few things to remember: A positive growth rate means the quantity is growing. How much will producers supply? Three types of graphs are used in this book: line graphs, pie graphs, and bar graphs. Our BSc Mathematics and Economics will prepare you for a postgraduate study and/or a career in a related field. Otherwise,he lay the scripture aside. The thin air at high altitudes explains why many mountain climbers need to use oxygen tanks as they reach the top of a mountain. Mathematical economics is a form of economics that relies on quantitative methods to describe economic phenomena. Poverty and Economic Inequality, Introduction to Poverty and Economic Inequality, 14.4 Income Inequality: Measurement and Causes, 14.5 Government Policies to Reduce Income Inequality, Chapter 15. Statistics, econometric theory, and then calculate what value of y.... Focus, this major will show you how to analyse problems clearly and based on simplifying assumptions, they. The types of graphs and briefly state when is most appropriate to use type! We also provide warnings about how graphs can show patterns as time,. The total, or healthcare providers to check whether a child ’ s physical development roughly. Out to nearly 600 data points very quickly from the graph are all easy, mathematics is used to data! 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