Table of Contents
- Lesson 1: The Nature of Demand
This lesson develops the economic tool of demand. Demand is determined by the value that people attach to a product (a good or a service). A demand curve is a graph with a negative slope that lies in the first quadrant. It illustrates the inverse relationship between the quantity of a product demanded and the price that people are willing and able to pay. A demand curve is most accurately derived from a demand schedule, which is a table of values relating prices to quantities demanded. To make this lesson appropriate for algebra I students, it will be restricted to the study of linear demand curves.
- Lesson 2: The Nature of Supply
This lesson develops the economic tool of supply. Supply is determined by the willingness and ability of producers to sell a product (a good or a service) at different prices. A supply curve is a graph with a positive slope in the first quadrant. It illustrates the direct relationship between the price of a product and the amount of product available for sale at each price. A supply curve is most accurately derived from a supply schedule, which is a table of values relating prices and quantities supplied. To make this lesson appropriate for algebra I students, it will be restricted to the study of linear supply curves.
- Lesson 3: Equilibrium: Determining Prices and Quantities
Supply and demand affect the prices people pay and the quantities they exchange in a market economy. Equilibrium is said to occur at the point at which quantity supplied equals quantity demanded. This point is at the intersection of the supply and demand curves. The point can also be found by solving the equations of the demand and supply curves simultaneously.
- Lesson 4: Understanding the Mathematics of Changes in Supply and Demand
This lesson asks students to look at the factors that cause a change in supply and/or a change in demand. Many factors influence the amount of a product that people are willing and able to purchase at each and every price. Such factors as income, tastes and preferences, the prices of related goods, the number of buyers, and expected future prices influence the demand for a product. When we observe a change in any of these factors, we normally expect to experience a change in demand for the product. A change in demand causes a parallel shift (or translation) of the demand curve. This is distinct from a movement along the demand curve, which (as noted in Lesson 1) is called a change in quantity demanded. A change in quantity demanded can only be caused by a change in the price of the product.
- Lesson 5: The Gains From Trade
This lesson is an application of the supply and demand tools developed in lessons 1-4. In the earlier lessons, models of supply and demand were introduced to show students how (equilibrium) prices are determined in markets. This analysis was also used to help students explain factors that caused a variation in market prices because of shifts in supply and/or demand curves. In this lesson, students learn that voluntary exchange between buyers and sellers results in gains for both. These gains from trade can be interpreted graphically as areas between the supply and demand curves. These regions are triangular when the curves are linear, which means the gains from trade can be calculated by finding the areas of triangles.
- Lesson 6: The Mathematics of Linear Economic Shapes: Slopes and Elasticities
As was noted in Lessons 1 - 4, a demand curve is used to describe the willingness and ability of buyers to purchase various quantities of goods and services at alternative prices. The visual representation of this relationship is a linear function in the first quadrant with a negative slope. This lesson explores a different way of representing the strength of the economic relationship between changes in price and quantity demanded along demand curves with different slopes.
- Lesson 7: The Mathematics of Nonlinear Economic Shapes: The Production Possibilities Curve
Because the resources (such as raw materials, minerals, energy, labor, equipment, machinery, etc.) that are used to produce goods and services are limited in their availability, we cannot have all that we want. When limited resources come into conflict with unlimited wants, scarcity is said to exist. Without scarcity, we could have all that we want, and we would not need to make difficult and costly choices. Because of scarcity, we must make choices, and choices are costly. In economics, cost (also referred to as opportunity cost) is defined as the highest valued alternative that must be forgone as a result of making a choice. For example, if one of your students is considering whether or not to join the school drum line, she must weigh the other alternatives that must be forfeited as a result of making this choice. These might include giving up a weekend job, having less time to do homework, or being unable to join the stage crew for the school play. The highest valued of these alternatives is the opportunity cost of joining the drum line. So, if the most valued alternative to joining the school drum line is having less time to do homework, then the student's opportunity cost of joining the drum line is giving up time to work on her studies.
- Lesson 8: The Mathematics of Nonlinear Economic Shapes: The Cubic Cost Function
Careful control of total cost is essential for a firm if it wishes to maximize profits. While many firm managers prefer to concentrate on the more glamorous activity of marketing and selling the company's product, many companies have gone bankrupt because of a lack of attention paid to the cost side of the profit-loss statement. In a world or scarcity, it is necessary for firms to economize on their use of precious productive resources. For a given level of production, the reward for success in containing costs in the marketplace is a profit. The penalty for failing to recognize the importance of limiting costs is an economic loss that could lead to bankruptcy.
- Lesson 9: Profit Mathematics
Most businesses in a market economy try to maximize profits. Economic profits are the difference between total revenue (the value of total sales for the business) and total cost (how much it costs the business to produce its goods or services). When total revenue exceeds total cost, then firms have earned a profit. Breakeven is said to occur when total revenue and total cost are equal. An economic loss arises when total cost is greater than total revenue.
- Lesson 10: Powerball Economics
In games of chance, such as a lottery, economists refer to a fair game as one in which the expected return from the game equals the amount that one must pay to play the game. If a lottery costs one dollar to play and the expected return from the play is one dollar, then it is a fair game. Most games of chance, such as state lotteries and casino games, are not fair in the sense that the payouts to winners are less than that which is taken in by the organizers of the contest. Most people prefer less risk to more risk. This helps to explain our willingness to pay for car, home, health, and other forms of insurance. We are willing to pay to be protected against the possibility that a low probability event (such as a fire, accident, or catastrophic illness) will occur. In competitive markets, insurance policies are likely to be fair in the sense that premiums equal the expected payout for the insured event. Thus people are willing to pay to insure against uncertainty, but they also appear to be willing to pay small amounts for the possibility (at extremely low probabilities) of winning very large sums of money. This is the principle upon which many state lottery games are based. This lesson looks at the economics of one such game, Powerball.
- Lesson 11: Cash or Annuity?
Jackpot winners of state lotteries may have the choice of receiving their winnings in the form of cash or an annuity. An annuity is a financial instrument that provides income at regular intervals over a specified time period. For example, New York's Lotto and California's SuperLotto offer an annuity with an annual payment for 26 years, and the multi-state Powerball lottery has a 25-year annuity option. Not many people will be lucky enough to win a lottery grand prize, but a great number of us will have a cash versus annuity option for receiving retirement distributions. These choices also exist for a number of other financial options, such as bonds and insurance accumulations. It is therefore important that students understand the economics of alternative payment options.
- Lesson 12: Autonomics
This lesson develops the idea of opportunity cost by examining the costs of owning and operating an automobile. Opportunity cost is the value of the next best alternative when a choice is made.
- Lesson 13: Tax Math
People pay a variety of taxes. Among the different types of taxes that we pay are the federal income tax and the payroll tax. How these taxes are applied has interesting economic implications. The income tax is a progressive tax. When a tax is progressive, the average rate of taxation is higher for higher-income earners than it is for lower-income earners. The payroll tax has two parts (Social Security and Medicare) and is primarily a proportional tax. For the most part, everyone pays the same tax rate on the payroll tax regardless of his/her level of income. However, since there is an earnings limit applied to one portion of the payroll tax, it is also a regressive tax over a range of earnings. That is, the average rate of taxation is higher for low-income earners than it is for high income earners.
- Lesson 14: The Mathematics of Savings
Because of interest compounding, establishing a commitment to personal savings early in one's professional career can yield large long-run benefits. This lesson looks at the mathematics that underlie the computations of the future value of savings. These computations are now commonly found at many on-line financial calculators. Students will see that relatively modest savings, when compounded over many years at rates of interest that appear to be historically achievable, can lead to the student being a multi-millionaire by the end of his or her working lifetime. The key is, of course, that students abstain from spending and commit to saving early on in their working life.
- Lesson 15: The Mathematics of Credit Card Interest and Fixed Payments
It is common for a high school student to receive multiple invitations to enroll for a credit card. In fact, an increasing number of high school students even carry credit cards. One goal of this lesson is to try to uncover some of the mathematics that underlies the calculation of numbers that are found on a monthly credit card statement. While these calculations are done using technology, it will likely help students understand the cost of maintaining balances on a credit card if they are to work out the numbers on their own. The first part of this lesson looks at the computation of the average daily balance on a credit card as well as monthly finance charges. It illustrates how hard it is to pay down a credit card balance when finance charges are carried from month to month and the minimum monthly payment is made. It also illustrates how paying down a credit card balance becomes even more difficult when the card is used to obtain additional credit from one month to the next.