(5.a.i) Opportunity cost—the good, the bad, and the ugly
Research has shown that less physically attractive people are more likely to commit crimes. This does not surprise the economist, who is quick to point to the concept of opportunity cost as an explanation. Data on people’s income, health, and happiness make clear that less attractive people make less money, experience poorer health, and experience higher rates of depression.
This means they have less to lose from going to jail. They do not leave behind the high paying job or the beautiful spouse. Some may find prison to be about the same or better than their normal life.
The definition of opportunity cost is: the value of the next best alternative. Committing the crime has a certain benefit, otherwise it would not be considered. The alternative to committing the crime is assurance you will not go to jail. The value of your non-prison life is higher for the attractive person, so the opportunity cost of crime to them is higher. Thus, they are more reluctant to break the law.
(ii) Opportunity cost—Roman soldiers
The Romans understood opportunity cost well. In the days of the Roman Republic they would conscript and give command to the wealthiest Romans for the important battles, under the assumption that a wealthy Roman has more to lose by fighting wars foolishly, and thus make better soldiers.(E1)
(iii) Opportunity cost—see Wilco in concert?
If you are given a free ticket to see Wilco, the cost of the concert is not free, it is what you would have done if you didn’t go to the concert, and how much you value that alternative. If you have nothing better to do, you go. If you have the opportunity to see a band you like better you might skip the Wilco concert, even if this preferred band costs money.
(iv) Opportunity cost—pesticides and radon
The concept of opportunity cost is essential for effective governance. For example, should we try to save lives by banning the use of pesticides in agriculture? Some studies suggest that banning all pesticides would cost us about $20 billion and save 20 deaths per year. That’s $1 billion per life saved. If you really want to save lives, use that $20 billion for radon testing in homes, which will save about 15,000 lives.(N1)
Thus, spending $20 billion to save 20 lives is a poor way to spend money, especially when you recognize that doing this forgoes the opportunity to spend that money for radon testing and save 15,000 lives.
Another consideration is the fact that banning pesticides would increase the price of fruits and vegetables, lowering consumption of these healthy foods and perhaps causing an increase in cancer rates (and other health problems). A wise government truly intending to improve health would not only consider the effects of eliminating use of pesticides, but also subsidizing fruits and vegetables.
Video 1—Ethicist Peter Singer on the opportunity cost of helping blind people (TED Channel, May 20, 2013)
(View entire TED talk at http://www.youtube.com/watch?v=Diuv3XZQXyc)
(v) Opportunity cost—the cost of raising crops
Suppose it costs a farmer $100 per acre to produce wheat and she receives revenues of $250 per acre. What is the cost of wheat production? Not $100, if we are talking about opportunity cost. She made a profit of $150 per acre growing wheat, but what profit could she have made growing the next most profitable crop? If the next best alternative is grain sorghum, and she could make $80 per acre, then the opportunity cost of wheat production is $80 acre.
Why do economists care more about opportunity costs than accounting costs? Because it’s opportunity costs that influences a person’s behavior. After all, if the opportunity cost of wheat production was $(20) (that means negative twenty dollars) per acre (because grain sorghum is more profitable) she wouldn’t grow wheat in the first place, regardless of wheat’s accounting cost of production.
(vi) What is your rate–of–return?
A few weeks ago, Mr. Lindstrom said similar land sold for nearly $11,000 an acre.
—Sullivan, Paul. August 16, 2013. “Despite Drop in Commodity Prices, Farmland Values Rise.” The New York Times.
Is Donald Trump a smart business–person? That is certainly his claim, but there is a compelling argument to the contrary. Forbes magazine claims he is worth about $4.5 billion. Now, that is a low of money, but consider the fact that when Trump began his career in 1976 he was worth about $200 million, and that was largely a gift from his father. Had he just invested that $200 million in the stockmarket since 1976, today he would be worth $12 billion (as opposed to his current actual worth of $4.5 billion).(M1) Compared to the opportunity cost of not investing his money in the stockmarket, Donald Trump actually loses large amounts of money over time. He may make profits, yes, but his economic profits are negative. (This of course assumes all the numbers cited above are correct.) Note that this does not assume that Trump invest well in the stock market. In fact, it assumes that he gives his money to someone else to invest in the stock market for him, and that he earns a rate–of–return equal to the stock market average.
Why did we assume that Trump’s opportunity cost of investing his money in his own private enterprises to be investing in the stock market? Because in truth we do not know what Trump’s real next best alternative is, but we know that anyone can invest in the stock market. Over long periods of time stocks are not very risky (though in short periods of time they are) and they earn a good return. Sometimes people assume the opportunity cost to be investing in a risk–free investment, like certificates–of–deposit.
Video 2—Better off just putting the money in a CD (certificate of deposit), from Silicon Valley
A rate–of–return is simply the change in the value of an investment over time, and is expressed as an annualized percentage of the original investment. On average, an investment in the stock market earns you a rate–of–return of about 8%, which means if you invest $1,000 in the stock market today that investment will probably be worth about $1,000(1.08) = $1,080. Certificates–of–deposits earn about 2%, so investing $1,000 in them will have a value of about $1,000(1.02) = $1,020 in one year.
Suppose you purchased ADM stock five years ago (assume today is March 26, 2017). During that five years the rate–of–return has been 7.25%, meaning every year your investment increases in value by about 7.25%. That sounds great, but on average other stocks earned a return of about 7.20%. ADM did indeed make money, but about the same amount of money as every other corporation. So if your economic profits assume that the next best alternative is to invest in the stock market in general, your economic profits are 7.25% - 7.20% = 0.05%.
(vii) When to harvest trees
Decisions about when to harvest trees involve a number of factors, one of these being opportunity cost. Suppose it is 2012. We have a stand of trees we must harvest by 2013, but we could harvest it now in 2012 . Imagine if we ignored opportunity costs and allowed trees to grow another year so long as the tree would actually increase in size and bring in higher accounting profits.
The table below shows the expected tree growth between 2012 and 2013. Allowing another year of growth adds 1,000 tons per acre of wood that can be harvested. If each ton provides $0.50 when harvested, then letting the trees grow until 2013 increases its value from $7,500 to $8,000. Waiting another year increases accounting profits attributable to trees by $500. If that was all that mattered, let the trees grow. But why would we concern ourselves only with money from the trees? Doesn’t money earned elsewhere matter also?
Now suppose we do consider opportunity cost, specifically, the fact that instead of letting the trees grow another year we could have harvested the trees in 2012, investing the profits at a real, risk-free rate of 8% (that 8% is an assumption I give you). To do this, we would harvest in 2012 and collect the $7,500 per acre of profits. This $7,500 then earns 8% interest between 2012 and 2013, thereby increasing our wealth from $7,500 to $8,100.
Clearly, it is better to harvest now, in 2012, as we prefer $8,100 in 2013 to $8,000.
Remember that opportunity cost is the value of the next best alternative. Letting the trees grow until 2013 would increase our accounting profits attributed to trees, but it ignores the opportunity cost of earning money elsewhere, and prevents us from maximizing our wealth from all potential sources.
Table 1—Tree harvesting decision
Column |
Column |
Column |
Column |
Column |
Year |
Age of stand in years |
Tons per acre, if harvested |
Accounting profits, if harvested this year
|
Accounting profits, if harvested last year
|
2012 |
20 |
15,000 |
($0.5 per ton)(15,000 tons per acre) |
———— |
2013 |
21 |
16,000 |
($0.5 per ton)(16,000 tons per acre) |
($7,500 from last year’s profits)(1.08) = $8,100 |
|
||||
By allowing the stand to grow from 20 to 21 years of age the value of the stand increases by ($8,000 - $7,500) = $500. There is an opportunity cost to letting the stand age. We could have harvested the trees at age 20 and invested it, earning an 8% interest rate. The total interest earned would be $7,500(0.08) = $600. Since the opportunity cost of letting the tree grow ($600) is greater than the increase in the value of the stand ($500), we maximize our wealth by harvesting the trees when the stand is 20 years old.
Now consider a more complex question. The basic question is the same, but now we are tasked when determining when to harvest the trees over a larger range of ages. You answer it just the same. Start at the youngest age of 28 years, in 2012. Ask yourself whether you would be richer in 2013 by letting the stand age or harvesting it now and investing it at the interest rate. If you let the stand age, then go to year 2013 and ask yourself whether you will be richer in 2014 by letting the stand age or harvesting the trees now and investing it at the interest rate.
As soon as it becomes more profitable to harvest the trees, you do it then and don’t worry about the latter years. If it is most profitable to harvest in, say, 2015, you never have to wonder whether it would have been better to wait until 2017, 2018, or later years.
Table 2—Another tree harvesting decision
Column |
Column |
Column |
Column |
Column |
Year |
Age of stand in years |
Tons per acre, if harvested |
Accounting profits, if harvested this year
|
Accounting profits, if harvested last year
|
2012 |
28 |
12,000 |
($0.15 per ton)(12,000 tons per acre) |
———— |
2013 |
29 |
14,800 |
$2,220 per acre |
($1,800 from last year’s profits)(1.03) = $1,854 |
2014 |
30 |
16,000 |
$2,400 per acre |
$2,286.6 |
2015 |
31 |
16,800 |
$2,520 per acre |
$2,472 |
2016 |
32 |
17,000 |
$2,550 per acre |
$2,595.6 |
|
||||
(viii) The magic of compound interest
Video 3—The magic of compound interest
(ix) Net Present Value
Video 4—Net present value
Application to state funding of pensions
Most states fund the pensions of their employees through promises and savings. If you are a public school teacher, the state will calculate how much money they will need to pay you in the future, and then they save and invest whatever amount of money is necessary to ensure your pension can be funded. For instance, if you are promised $60k in twenty years, the government will invest however much money will accumulate to $60k in twenty years (both numbers adjusted for inflation).
Lately states have not been setting aside enough money, and thereby are seriously underfunding their pensions. The error—though mind you, the error is deliberate—is to assume the state's investments will earn a 7.5% real interest rate, whereas in reality a rate of 2-4% is more realistic. To see how this error results in an underfunding of pensions, consider how much money needs to be set aside to secure you the $60k in 20 years you were promised, using Net Present Value (NPV). Using the unrealistic 7.5% rate, determine the Net Present Value of $60k in 20 years in today's dollars.
[1] NPV = ($60,000)(1.075)(-20) = $14,124.79
Now calculate the NPV using the realistic rate of 3%.
[2] NPV = ($60,000)(1.00)(-20) = $33,220.55
Due to an inaccurate discount rate the government only saves half the money it needs to fund your pension. This is a problem plaguing most all states and municipalities, and the problem is not just that they choose a poor discount rate, but that the voters let them get away with it.
Few fiscal problems are as grave, or little understood, as underfunded state and municipal pensions. The funding
gap for all state schemes is estimated at $4 trillion—[which is] 25% of [the nation's] GDP.
...
In Illinois [pensions] are only 40% funded; in New Jersy 53%...
—The Economist. June 15, 2013. Ruinous promises. Page 13.
Video 5—SEE THE SIMPSONS ILLUSTRATE NET PRESENT VALUE
References
(C1) Cutler, David M., E. L. Gleaser, and J. Shapiro. 2004. "Why have Americans become more obese? Journal of Economic Perspectives. 17(Summer):93-118.
(E1) Everitt, Anthony. 2012. The Rise of Rome. Random House: NY, NY.
(G1) Groening, Matt [creator].Jean, Al. [Executive Producer]. Maxtone-Graham, Ian, John Frink James L.Brooks, Matt Groening, Matt Selman, and Sam Simon [producers]. O'Brien [writer]. Polcino, Dominic [director]. August 23, 1998. "Lard of the Dance." The Simpsons. Gracie Films and 20th Century Fox Television [Production companies]. 20th Television [distributor].
(M1) McEwan, Melissa. September 21, 2016. ’Donald Trump’s self-proclaimed business expertise was casually demolished in a sentence.“
(N1) Norwood, F. Bailey and Jayson L. Lusk. 2008. Agricultural Marketing and Price Analysis. Pearson / Prentice-Hall: NY, NY.
(N2) National Geographic. October 8, 2013. Extreme Obesity. Accessed October 13, 2013 at http://www.youtube.com/watch?v=NfxFn1IqHo4&list=TLFS81vSgu3fwCv0R-g0YX5ZEnoi0YfjZi.
(T1) Taylor, Timothy. 2011. Unexpected Economics [lectures]. Lecture 20: Obesity—Who Bears the Costs? The Great Courses. The Teaching Company.