Economics Lecture Twelve
Traditionally there were four ways to make money:
- Perform labor to earn wages. This is how most people make most of their money.
- Invest capital to earn interest. This is what you can do once you save up some money.
- Allow someone to use your land in exchange for rent.
- Start a new business to earn profits. But watch out here: 9 out of 10 new businesses fail!
Sounds simple enough, right? Look around you, and you’ll see people earning money each of the four above ways. Mostly, you’ll see the first way: get a job and earn some wages. That entails the least risk and is the easiest for most people. Adults and teenagers often follow the path of least resistance, and often imitate others. In economics, that means getting a job to work for a company. It’s great until the economy goes through a downturn and you get "laid off" (fired), or the job becomes tiresome and tedious, or the boss fires you because he did not like something you said. Then it’s not so great anymore. But as a teenager you can earn money from someone else while you are learning how business works. You need experience and savings before you can even try to make money the other three ways.
Economists have their own terminology which, as you’ve seen in this course, is often different from common usage. In economics, the basic terms of wages, interest, rent and profit are all redefined. Here we go:
“Economic wages” are payments for the worker’s opportunity cost of time. When a student earns $7 per hour working for a dry cleaners, those wages are payments for his opportunity cost of time. He could be working someone else making money. The market rate of $7 implies that his time is worth that much at this stage in his life.
“Economic rent” is the payment for a perfectly inelastic input. If increasing the payment does not increase the supply of the input, then this extra amount above cost is a “rent”. It is similar, but not identical, to rent paid on scarce land. Increasing the rent does not increase the supply the land. The supply is fixed. Don’t worry if you don’t understand this yet. We’ll spend more time on it below.
“Interest” is straightforward: it is the cost of the use of money over time. If you borrow $10,000 for your business, then you have to pay interest (say 5% per year) for using that money. The person who lent you the money wants something for it. He’s not going to give it to you for free.
“Economic profits” is concept we’ve addressed before. It is total revenues minus total costs, including opportunity costs of time and money in the costs.
“There’s no free lunch,” according to the famous saying. “It costs money to make money” is another aphorism. Most bank's ATMs charge $2 or $3 just to withdraw cash from your account at a different bank.
If you asked me to loan you $1000, then I might answer: why? What’s in it for me? You would then say that you promise to give it back. I would then say why should I give it to you in the first place? If I just keep the money, then I won’t have to worry about your giving it back.
You would then offer to pay me extra money in exchange for loaning you $1000. We would bargain. You might offer me $25. I might reply that is not enough for me to go the trouble and take the risk to loan you $1000. Then you might offer me $50. I might wonder if I can get a better deal somewhere else. Ultimately we might settle on an amount that makes it worthwhile for me and advantageous for you. Some states have limits on how much interest can be charged. Query: should laws limit the amount of interest that can be charged?
If I agreed to loan you $1000 for an extra payment by you of $50, then the interest rate would be $50/$1000 = 5%. Usually rates are stated in annual terms. Requiring an extra $50 in interest after one year, on top of the repayment of the "principal" of the original $1000, is the equivalent of an interest rate of 5% per year.
The concept of "compounded interest" refers to earning interest on the interest. "Compounded yearly" or "compounded annually" means that the interest is added to the total amount due at the end of the year, and then the interest for the next year is calculated by including the interest for the first year. Here is an example:
- $1000 is loaned to you today at an interest rate of 5%, compounded annually.
- After one year, the amount due is $1000 plus 5% of $1000, for a total of $1050.
- After two years, the amount due is $1050 plus 5% of $1050, for a total of $1102.50, because the interest on the first year is included in calculating the interest for the second year.
The opposite of "compounded" interest is "simple" interest. In the above example, the total amount due the second year is $1000 plus 5% of $1000 (for the first year) plus another 5% of only the original $1000 (for the second year), for a total of $1100. Notice how the total amount under compounded interest is always larger than the total amount using simple interest.
If you are saving money, then you want as much compounding of the interest as possible. Ideally, you would like the interest on the money you save to be "compounded daily," such that each day's interest is on a total amount that includes all the interest that has accumulated for prior days.
Sometimes people repay money all at once, rather than with interest payments. Suppose I gave you $1000 and you promised to pay me back $1500 in 10 years. Then economists ask, what is the “rate of return” or “yield” on that investment?
That is more difficult to calculate. I am receiving 50% return on my investment, but ten years from now. At first glance, you may think to simply divide 50% by 10 years to calculate a rate of return of 5% per year. That is a rough approximation, but not entirely precise.
What is wrong with it? The flaw is that it fails to address the time value to money. We explain that next.
The Time Value of Money
Suppose I told you that I will be giving you $100, but that you have a choice: either (1) I will give you the $100 today, or (2) I will give it to you in two years. Which would you prefer?
Today, of course. But why? Is the $100 really worth more today than in two years in the future?
Yes, it is. You could take $100 today and invest it, and have it grow to more than $100 in two years. Or you could buy something with it that you could enjoy for the two years. Or you could give it to a charity that could make good use of it for the two years.
Money, like anything else, has an opportunity cost. Just as it is a waste of your time to sit and watch television for a few hours, it is a waste of money to have it sit idle without earning anything for several years. At a minimum, it could be earning interest.
This was explained by Jesus in His Parable of the Talents, in Matthew 25:14-30 (RSV):
- For it will be as when a man going on a journey called his servants and entrusted to them his property; to one he gave five talents, to another two, to another one, to each according to his ability. Then he went away.
- He who had received the five talents went at once and traded with them; and he made five talents more. So also, he who had the two talents made two talents more. But he who had received the one talent went and dug in the ground and hid his master's money.
- Now after a long time the master of those servants came and settled accounts with them. And he who had received the five talents came forward, bringing five talents more, saying, 'Master, you delivered to me five talents; here I have made five talents more.' His master said to him, 'Well done, good and faithful servant; you have been faithful over a little, I will set you over much; enter into the joy of your master.' And he also who had the two talents came forward, saying, 'Master, you delivered to me two talents; here I have made two talents more.' His master said to him, 'Well done, good and faithful servant; you have been faithful over a little, I will set you over much; enter into the joy of your master.' He also who had received the one talent came forward, saying, 'Master, I knew you to be a hard man, reaping where you did not sow, and gathering where you did not winnow; so I was afraid, and I went and hid your talent in the ground. Here you have what is yours.' But his master answered him, 'You wicked and slothful servant! You knew that I reap where I have not sowed, and gather where I have not winnowed? Then you ought to have invested my money with the bankers, and at my coming I should have received what was my own with interest. So take the talent from him, and give it to him who has the ten talents.
- For to every one who has will more be given, and he will have abundance; but from him who has not, even what he has will be taken away. And cast the worthless servant into the outer darkness; there men will weep and gnash their teeth.
Jesus was concerned with something far greater than money. But the point applies to money also: money does have a time value to it. Money tomorrow is not worth as much as the same amount of money today.
How can you compare future money to present money? By calculating the “present value of money.” That is how much one would need in the present which, with investment, would equal the proposed future payment. We use the interest rate to determine how much something today should be worth in the future, or how much a payment promised in the future is worth today.
If I promise to give you $100 in 5 years, and the interest rate is 5% annually, then ask yourself how much you would need today to generate that same $100 in 5 years. It would be less than $100, because you could earn interest on it. In fact, you would only need $100 divided by (1.05) times itself 5 times (i.e, 1.05 x. 1.05 x 1.05 x. 1.05 x. 1.05)
Using a calculator, that comes to $78.35. That’s amazing, isn’t it? Receiving $100 in 5 years is equivalent to only $78.35 today, assuming an interest rate of 5%.
We can check our work. If you had $78.35 today and you invested it the bank at an interest rate of 5%, then next year it would be worth 5% more: $78.35 x 1.05 = $82.27
You would do the same thing in the second year, investing it for a return of 5%: $82.27 x 1.05 = $86.38
And again in year three: $86.38 x 1.05 = $90.70
And again in year four: $90.70 x 1.05 = $95.24
And, finally, one more time for the fifth year: $95.24 x 1.05 = $100
So $100 to be paid five years from now is the same thing as receiving only $78.35 today. That’s due to the effect of the time value of money.
Using the time value of money, now we can make investment decisions. As an owner of a company or merely someone wanting to see your savings grow, you will need to make investment decisions.
Suppose your widget company is considering a new machine that will last for two years and costs $3500. Suppose also that it will be worthless afterward. Suppose further that it will bring in revenue of $2000 per year, and that interest rates are 10%. Should you invest in the machine?
Ask yourself what the time value of the added income is. It equals:
- ($2000/1.10) + ($2000/(1.10x1.10)) = $1818.18 + $1652.89 = 3471.07
Look again at its cost. What is your best decision? Don’t buy it.
Read this lecture and look at some of the problems on the midterm exam. The homework assignment is light this week to give you time to spend reviewing concepts in this course. Then answer the problems below:
Answer 5 out of 6:
1. If you were to loan someone money, why would you want him to pay you something extra (interest) when he pays back the loan? Give at least one reason.
2. Suppose I loaned you $1000 today, and interest rates are 5% per year (compounded annually), and you repaid the loan plus interest in 2 years, then what is the total you would pay to satisfy this debt?
3. Review: is the cost of the bus for a trip to D.C. a "fixed cost" or a "variable cost"? Explain, assuming for the purpose of this question that one and only one bus can be used (in reality, we may have several buses).
4. Which concept in Economics do you think is the best self-motivator, which you might use to achieve more?
5. Suppose I will pay you $1000 in two years, and the interest rate is 10% per year, compounded annually. How much should you pay me today to receive $1000 in two years? Show your work.
6. Pick another question from the midterm exam that you answered incorrectly, and explain the correct answer.
Answer 3 out of 4:
7. Explain what “economic rent” is in your own words, using your own example.
8. An agreement by different firms with each other to reduce output is illegal. Why should that be illegal?
9. What is your favorite concept in Economics, and why?
10. Nash equilibrium, revisited: What is the Nash equilibrium for two gas stations (an oligopoly) that are situation immediately across the street from each other? In other words, what price do they sell at, expressed in terms of one of their cost measures? Explain the process that reaches that "equilibrium".