**Income, Saving, and Investment**

Income refers to the flow of new consumer goods (and services) that an individual has the potential to acquire during a period of time.6 Saving occurs when someone consumes less than his income; it is “living below one’s means.” Investment occurs when ingredients of production are devoted to future income, rather than immediate consumption.

In Lesson 10 we will discuss in much greater detail the relationship between income, saving, and investment in a modern market economy, in which most exchanges involve money. For now, we quickly illustrate that these advanced concepts have their analogs even in the simple Crusoe economy.

It’s easiest to explain with a numerical example. Obviously the following numbers are chosen for simplicity, and serve only to make the scenario concrete enough so that you can really think through the types of tradeoffs Crusoe faces. In that light, suppose that with his bare hands, Crusoe can find an appropriate tree to climb and knock down 1 coconut per hour. If Crusoe devotes 10 hours per day to work, while leaving the rest for leisure (which includes sleep), that means his raw labor can extract 10 coconuts per day from the natural resources available to him on the island. Fortunately, eating 10 coconuts per day provides enough nourishment to maintain Crusoe in decent health. But working 10 hours per day, with no weekend, is hardly an ideal lifestyle. Besides the grueling schedule, Crusoe knows that if he should ever become sick or injured, he could easily die because of the vulnerability of his hand-to-mouth existence.

There is a solution. Crusoe is a disciplined and resourceful man, and realizes that the ability to save and invest can greatly improve his standard of living. Soon after assessing his situation on the island, Crusoe begins saving 20% of his income every day. In other words, Crusoe continues to work 10 hours per day, day in and day out, gathering (earning) 10 coconuts per day. But he only eats (consumes) 8 coconuts each day, and sets aside (saves) 2 coconuts out of each day’s income.

After living below his means in this fashion for 25 days, Crusoe has accumulated a stockpile of 50 coconuts. From that point on, he once again resumes eating 10 coconuts per day—he consumes his full paycheck every day, as it were. The main reason Crusoe stopped accumulating additional coconuts is that he discovered their taste begins to suffer five days after being knocked down from the tree. Therefore, Crusoe has settled into a comfortable routine: Every day he picks a fresh batch of 10 coconuts and adds them to one side of his stockpile. During the day, he eats the oldest 10 coconuts from the other side of his stockpile. With this rotation, Crusoe still enjoys a full 10 coconuts (which still taste pretty good) per day, but he also has a savings fund of 50 coconuts that he can draw down in case of emergency. For example, if Crusoe should come down with a tropical illness that makes him unable to work, he has enough saved up to eat for ten days on half-rations.7 Because of his willingness to put in hard work and save its (literal) fruits, Crusoe has greatly enhanced his material position compared to his original situation. Rather than living on the edge of starvation, Crusoe now has a buffer of ten days.

The simple act of saving and accumulating consumption goods is very useful, but Crusoe realizes he can do much better. After surveying the materials at his disposal, Crusoe sets out to invest his savings in a long-range venture, which he expects will permanently increase his future flow of daily income. Relying on his stockpile of 50 coconuts, Crusoe decides to take two days off from climbing trees to knock down new coconuts for the stockpile.

But our hero isn’t taking a much needed vacation! On the contrary, Crusoe spends the first day—all 10 hours—wandering the island, gathering branches of the appropriate length and thickness. The process is slow-going, because when Crusoe spies a good candidate, he needs to use a sharp rock to saw away at the branch, before he can safely snap it off the tree without ruining it.8 During this day, Crusoe eats 10 coconuts, reducing his stockpile down to 40. Even though he has worked all day, he has no new coconuts to show for it. Instead, he has only a collection of sturdy and long branches, which he has transformed from their original shape and location.

During the second day, Crusoe spends another 5 hours using sharp rocks to further prepare the branches. Then he spends 2 hours cutting down vines and bringing them back to camp. Finally, in the remaining 3 hours of the second workday, Crusoe lays the branches on the ground, end-to-end but with a large degree of overlap. Then he uses the vines to tie the branches snugly to each other. At the end of the second day, Crusoe’s stockpile has dwindled to 30 coconuts. But in addition to this (shrinking) stockpile of savings, Crusoe has a new capital good: A long and sturdy pole.

The next day Crusoe takes his capital good out for a spin. He discovers with great satisfaction that in a single hour, his labor power—aided by the new capital good—can yield 5 coconuts. This is such a tremendous boon to his productivity that Crusoe now decides he’s been working too much! Rather than working 10 hours per day gathering food, Crusoe now spends only 4 hours per day knocking them down. This brings in a daily flow of 20 coconuts per day, twice what he was “earning” with his bare hands. Wanting to replenish his stockpile to the fullest amount that still allows for tasty coconuts, Crusoe saves some of his new earnings for a few weeks, until his stockpile has grown to 100 coconuts.9 He once again has five days’ worth of full-rations, except now a “full-ration” means 20 coconuts per day. In the new equilibrium, Crusoe spends 4 hours per day knocking down 20 new coconuts, which he adds to the stockpile. During that same day, he eats the 20 oldest (ripest) coconuts in the stockpile.

Things are obviously looking up for Mr. Crusoe. Before, he had to put in 10 hours per day of fairly intensive work; it’s hard to climb trees all day. In exchange for all that toil, Crusoe enjoyed 10 coconuts each day. But after his wise investment in the construction of a capital good, Crusoe finds that he only needs to spend 4 hours per day knocking down coconuts with the pole—a much easier task than climbing a tree and grabbing them with his bare hands. He also gets to enjoy twice as many coconuts per day as before, which is frankly the upper limit of how many coconuts he would want to eat.

There is one more important detail. If Crusoe wants to permanently maintain his new, higher standard of living, he can’t enjoy 20 hours of leisure per day. No, in addition to spending 4 hours per day laboring in the collection of new coconuts, Crusoe must also devote some of his scarce time to the maintenance of his pole. For example, suppose that after using the pole for a full week, the component branches wriggle out of their tight knots, and each end of the pole is quite battered. What this means is that after the seventh day of using his brand new capital good, Crusoe will need to devote some time to replacing the two end branches, as well as re-wrapping the entire pole with new vines.

Now if Crusoe only works the minimum 4 hours per day, collecting coconuts, he can only get away with this slacking for seven days. On the morning of the eighth day, Crusoe would find himself with a useless pole, and he would have to spend (let’s say) 7 hours on that day, working to collect new vines and two new branches, and to assemble the new pole. Moreover, in addition to working so many hours, Crusoe would have to draw down on his coconut stockpile, since he wouldn’t be able to gather any new coconuts that day.

Rather than engage in this volatile schedule—seven days of light work with many coconuts, with an eighth day of intense work and no income, Saving, and Investment

We now know that Crusoe can separate his world into various types of scarce objects, in the categories of natural resources, labor, capital goods, and consumer goods (which include leisure). Connecting all of these is the flow of time, and Crusoe’s understanding of how his actions now can alter his happiness in the future. Specifically, Crusoe can choose to save and invest today, in order to raise his future income.

Income refers to the flow of new consumer goods (and services) that an individual has the potential to acquire during a period of time.6 Saving occurs when someone consumes less than his income; it is “living below one’s means.” Investment occurs when ingredients of production are devoted to future income, rather than immediate consumption.

In Lesson 10 we will discuss in much greater detail the relationship between income, saving, and investment in a modern market economy, in which most exchanges involve money. For now, we quickly illustrate that these advanced concepts have their analogs even in the simple Crusoe economy.

It’s easiest to explain with a numerical example. Obviously the following numbers are chosen for simplicity, and serve only to make the scenario concrete enough so that you can really think through the types of tradeoffs Crusoe faces. In that light, suppose that with his bare hands, Crusoe can find an appropriate tree to climb and knock down 1 coconut per hour. If Crusoe devotes 10 hours per day to work, while leaving the rest for leisure (which includes sleep), that means his raw labor can extract 10 coconuts per day from the natural resources available to him on the island. Fortunately, eating 10 coconuts per day provides enough nourishment to maintain Crusoe in decent health. But working 10 hours per day, with no weekend, is hardly an ideal lifestyle. Besides the grueling schedule, Crusoe knows that if he should ever become sick or injured, he could easily die because of the vulnerability of his hand-to-mouth existence.

There is a solution. Crusoe is a disciplined and resourceful man, and realizes that the ability to save and invest can greatly improve his standard of living. Soon after assessing his situation on the island, Crusoe begins saving 20% of his income every day. In other words, Crusoe continues to work 10 hours per day, day in and day out, gathering (earning) 10 coconuts per day. But he only eats (consumes) 8 coconuts each day, and sets aside (saves) 2 coconuts out of each day’s income.

After living below his means in this fashion for 25 days, Crusoe has accumulated a stockpile of 50 coconuts. From that point on, he once again resumes eating 10 coconuts per day—he consumes his full paycheck every day, as it were. The main reason Crusoe stopped accumulating additional coconuts is that he discovered their taste begins to suffer five days after being knocked down from the tree. Therefore, Crusoe has settled into a comfortable routine: Every day he picks a fresh batch of 10 coconuts and adds them to one side of his stockpile. During the day, he eats the oldest 10 coconuts from the other side of his stockpile. With this rotation, Crusoe still enjoys a full 10 coconuts (which still taste pretty good) per day, but he also has a savings fund of 50 coconuts that he can draw down in case of emergency. For example, if Crusoe should come down with a tropical illness that makes him unable to work, he has enough saved up to eat for ten days on half-rations.7 Because of his willingness to put in hard work and save its (literal) fruits, Crusoe has greatly enhanced his material position compared to his original situation. Rather than living on the edge of starvation, Crusoe now has a buffer of ten days.

The simple act of saving and accumulating consumption goods is very useful, but Crusoe realizes he can do much better. After surveying the materials at his disposal, Crusoe sets out to invest his savings in a long-range venture, which he expects will permanently increase his future flow of daily income. Relying on his stockpile of 50 coconuts, Crusoe decides to take two days off from climbing trees to knock down new coconuts for the stockpile.

But our hero isn’t taking a much needed vacation! On the contrary, Crusoe spends the first day—all 10 hours—wandering the island, gathering branches of the appropriate length and thickness. The process is slow-going, because when Crusoe spies a good candidate, he needs to use a sharp rock to saw away at the branch, before he can safely snap it off the tree without ruining it.8 During this day, Crusoe eats 10 coconuts, reducing his stockpile down to 40. Even though he has worked all day, he has no new coconuts to show for it. Instead, he has only a collection of sturdy and long branches, which he has transformed from their original shape and location.

During the second day, Crusoe spends another 5 hours using sharp rocks to further prepare the branches. Then he spends 2 hours cutting down vines and bringing them back to camp. Finally, in the remaining 3 hours of the second workday, Crusoe lays the branches on the ground, end-to-end but with a large degree of overlap. Then he uses the vines to tie the branches snugly to each other. At the end of the second day, Crusoe’s stockpile has dwindled to 30 coconuts. But in addition to this (shrinking) stockpile of savings, Crusoe has a new capital good: A long and sturdy pole.

The next day Crusoe takes his capital good out for a spin. He discovers with great satisfaction that in a single hour, his labor power—aided by the new capital good—can yield 5 coconuts. This is such a tremendous boon to his productivity that Crusoe now decides he’s been working too much! Rather than working 10 hours per day gathering food, Crusoe now spends only 4 hours per day knocking them down. This brings in a daily flow of 20 coconuts per day, twice what he was “earning” with his bare hands. Wanting to replenish his stockpile to the fullest amount that still allows for tasty coconuts, Crusoe saves some of his new earnings for a few weeks, until his stockpile has grown to 100 coconuts.9 He once again has five days’ worth of full-rations, except now a “full-ration” means 20 coconuts per day. In the new equilibrium, Crusoe spends 4 hours per day knocking down 20 new coconuts, which he adds to the stockpile. During that same day, he eats the 20 oldest (ripest) coconuts in the stockpile.

Things are obviously looking up for Mr. Crusoe. Before, he had to put in 10 hours per day of fairly intensive work; it’s hard to climb trees all day. In exchange for all that toil, Crusoe enjoyed 10 coconuts each day. But after his wise investment in the construction of a capital good, Crusoe finds that he only needs to spend 4 hours per day knocking down coconuts with the pole—a much easier task than climbing a tree and grabbing them with his bare hands. He also gets to enjoy twice as many coconuts per day as before, which is frankly the upper limit of how many coconuts he would want to eat.

There is one more important detail. If Crusoe wants to permanently maintain his new, higher standard of living, he can’t enjoy 20 hours of leisure per day. No, in addition to spending 4 hours per day laboring in the collection of new coconuts, Crusoe must also devote some of his scarce time to the maintenance of his pole. For example, suppose that after using the pole for a full week, the component branches wriggle out of their tight knots, and each end of the pole is quite battered. What this means is that after the seventh day of using his brand new capital good, Crusoe will need to devote some time to replacing the two end branches, as well as re-wrapping the entire pole with new vines.

Now if Crusoe only works the minimum 4 hours per day, collecting coconuts, he can only get away with this slacking for seven days. On the morning of the eighth day, Crusoe would find himself with a useless pole, and he would have to spend (let’s say) 7 hours on that day, working to collect new vines and two new branches, and to assemble the new pole. Moreover, in addition to working so many hours, Crusoe would have to draw down on his coconut stockpile, since he wouldn’t be able to gather any new coconuts that day.

Rather than engage in this volatile schedule—seven days of light work with many coconuts, with an eighth day of intense work and no coconuts—Crusoe can smooth things out. In a typical day in the new equilibrium, he can spend 4 hours knocking down 20 new coconuts to add to his stockpile (while of course eating the ripest 20 from the same stockpile of 100). But then he also spends a fifth hour each day working on the preservation of his capital good. This way, after seven days have passed in a typical week, Crusoe will have performed the 7 hours’ worth of labor necessary to restore the pole after it has been worn down from a week of usage.

In the jargon of economics, we can step back and describe what Crusoe has done. By consuming less than his daily income—by living below his means—Crusoe saved coconuts in order to build up a fund to guard against sudden disruptions in his future income. Moreover, Crusoe then invested his resources into the creation of a capital good that greatly augmented his labor productivity. After the completion of the pole, Crusoe only consumed his net income each day, because he invested enough of his gross income to just balance the depreciation of his capital good.

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