EBF 200
Introduction to Energy and Earth Sciences Economics

 

A Desert Island Economy

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I am tempted to start the course by trying to say "what economics is" and so on, but it is perhaps easiest to start with a simple illustration.

Imagine you are on a desert island. There are two things you can eat on this island: coconuts and fish. If you wish to survive, you spend all of the available daylight trying to catch fish or harvest coconuts from the palm trees. We can assume, for the time being, that all of your day is taken up doing one of these two things. You need to divide your day between gathering coconuts and catching fish, since a diet of just one or the other is not healthy. Suppose you have 10 hours a day to work. It takes you one hour to catch a fish, and climbing a tree to get a coconut takes half an hour. So, in 10 hours you can catch 10 fish, or you can gather 20 coconuts. You could also do a bit of both: maybe spend 8 hours fishing and 2 hours getting coconuts, which would give you 8 fish and 4 coconuts. After a few weeks on the island you settle on a balance whereby you spend 7 hours a day catching fish and 3 hours harvesting coconuts. This gives you 7 fish and 6 coconuts per day. If you want more fish, you have to give up some coconuts, and if you want more coconuts, you have to give up some fish, because there are only a certain number of hours in a day, and you can't make more daylight!

Now, what if it turns out that you are not alone on this island. Suppose there is a person who happens to go by the name "Friday." He's been on the island a long time and has gotten good at fishing. It turns out that he can catch a fish in 20 minutes, but it also takes him half an hour to climb a tree and harvest a coconut. Friday has gotten into a routine where he fishes for 4 hours a day, catching 12 fish, and he harvests coconuts for 6 hours, getting 12 coconuts per day.

This is getting a little complicated, so we'll summarize:

  • You: 7 fish, 6 coconuts per day.
  • Friday: 12 fish, 12 coconuts per day.
  • Total: 19 fish, 18 coconuts.
line drawing of a boy fishing with a stick.

Now, let's suppose that one day, you and Friday meet up for the first time. After a bit of discussion, you start talking about food, and how much food you get each day. You both work 10 hours per day, and get a total of 19 fish and 18 coconuts.

What if I said that it was possible for both of you to get more fish and more coconuts, and neither of you had to work longer hours? Is this magic? Well, not quite.

Let's say you decided to spend all of your day harvesting coconuts, meaning that you were able to get 20 in a day.

At the same time, Friday spends 8 hours fishing. He is able to catch 24 fish and gets 4 coconuts in the other two hours.

Now, between the two of you, you have 24 fish and 24 coconuts. You have more fish AND more coconuts

So, collectively, you are better off. However, neither of you likes the proportion of things you have yourself. You have too many coconuts and not enough fish. Friday does not have enough coconuts. What you can do then is make a trade. Let's say you trade away 10 coconuts in exchange for 10 fish. Now you have 10 coconuts and 10 fish. Friday has 14 coconuts and 14 fish.

line drawing of a palm tree with coconuts.

Let's summarize:

  • Before you meet, 7 fish and 6 coconuts.
  • After you meet, 10 fish and 10 coconuts.

Friday:

  • Before you meet, 12 fish and 12 coconuts
  • After you meet, 14 fish and 14 coconuts.

So, after meeting, you both have more fish and more coconuts. How has this happened? Is this some kind of magic? As I said before, not quite.

The above story may seem a little simplistic - it is - but it powerfully illustrates some important topics that we talk about in the field of economics. What has happened? Well, the first thing that happened after the meeting of you and Friday is that you decided to specialize. You decided to do what you are good at - gathering coconuts. Friday concentrated most of his time on what he is good at - catching fish. By each focusing on what you are good at, you became more efficient. You then decided to trade. Specialization and trade made you both better off, and made the sum of the two of you better off.

Complicated? Of course! So, let’s do some more examples.

Example: Comparative Advantage and the Robinson Crusoe Economy

  • Robinson Crusoe is stuck on a desert island to fend for himself. He can gain two goods, fish and coconuts.
  • In any one day, he can gain 0 coconuts and 8 fish, 1 C and 6 fish, 2 C and 4 fish, and so on down to 4 C and 0 fish. In mathematical terms, Rob can get 2C + F = 8, where C stands for coconut and F for fish (C and F non-negative). Rob maximizes his happiness, and let us assume (somewhat arbitrarily) he chooses 3 C and 2 F.
Table 1.1 Robinson Crusoe Economy
Rob's Choice Coconuts Fish
#1 0 8
#2 1 6
#3 2 4
#4 3 2
#5 4 0

What is Rob's opportunity cost of coconuts? 2 fish

What is Rob's opportunity cost of fish? 0.5 coconuts

Rob Meets Friday

It turns out that Friday is living on the other side of the island. Friday has a "production function" such that C + F =4.

Table 1.2 Friday's Choice
Friday's Choice Coconuts Fish
#1 0 4
#2 1 3
#3 2 2
#4 3 1
#5 4 0

Living by himself, Friday chooses 2 C and 2 F.

What is Friday’s opportunity cost of coconuts?

Of fish?

Can Rob and Friday make each other better off?

YES THEY CAN,

  • Assume (for example) Friday makes only coconuts: 4C and 0F. Rob makes 1C and 6F. (So, they specialize.)
  • Now together they have 5C and 6F - more than they had separately.
  • Assume Rob trades 2.5 fish to Friday for 2 coconuts. Now are they both better off?
  • Rob now has 3C and 3.5F. Before he met Friday he had 3C and 2F. So, he is better off, since he is greedy, and therefore more goods are preferred to less.
  • Friday has 2C and 2.5F. Before he met Rob he had 2 of each. So, he is better off.
  • So, both Rob and Friday gain from trading – even though Friday wasn’t better than Rob at anything!

Note the 4 Step Approach

  1. Figure out each party’s opportunity cost;
  2. Figure out each party’s comparative advantage;
  3. Determine which good each party should specialize in, and determine production.
  4. Have the 2 parties trade to make each better off.

Remember, More is Better Than Less!

Example: Comparative Advantage Rosie and Donald

Rosie O’Donnell and Donald Trump are stuck on a deserted island. Rosie has production function 3T+B=20, where T is the production of turtles and B the production of bananas. The Donald has production function T+6B=25. If they could not trade with each other, Rosie would choose to produce 3 turtles, and the Donald would produce 13 turtles.

Figure out a possible production/allocation system where both the Rosie and the Donald would be better off trading than not trading.

Rosie has production function 3T+B=20, which implies that each turtle cost 3 bananas. She chooses T=3, which implies that (3*3)+B=20, B=11.

The Donald has production function T+6B=25, which implies that each turtle costs 1/6th of a banana. The Donald chooses T=13, so, B=2.

Turtles are much cheaper for the Donald rather than Rosie (1/6th of a banana vs. 3 bananas). So, Donald should trade turtles to Rosie for bananas.

Many trades/production decisions are possible.

Assume Rosie makes all bananas. Since for her, 3T+B=20, she makes 20 bananas.

If Donald makes all turtles, he makes 25 turtles.

So, we now have B=20, T=25.

Without trade B=11+2=13, T=13+3=16. So, now we have more production of each.

So, now assume that The Donald trades 6 turtles for 5 bananas.

The Donald now has T=25-6=19, B=0+5=5. Before, he had T=13, B=2. So, he is better off because he has more of both.

Rosie now has T=0+6=6, and B=20-5=15. Before, she had T=3, B=11. So, she is better off.

Both parties gain from trading!

Practice Question from Final Exam

Eric and Rod are stuck on a desert island. There are two goods, fish (F) and coconuts (C). Eric has production function F+C=20, and without trading chooses C=12. Rod has production function F+2C=30 and without trading chooses C=11. Explain an arrangement that can make both better off. Make sure you don’t fall into the trap!

Click here for answer

If Eric chooses C=12, that implies F=8.

If Rod chooses C=11, that implies F=8. Total w/o trading C=23, F=16.

Rod has the comparative advantage in fish, and Eric has the comparative advantage in coconuts. So, Rod should specialize in fish and Eric in coconuts.

However, full specialization does not produce enough coconuts. (This is the trap!)

So, let Eric make C=20. We still need 3 C, so Rod makes 3 C and 24 F.

Eric then trades 8 C to Rod for 12 Fish.
Eric now has C=12 and F=12. He is better off.
Rod has C=11 and F=12. He is better off.

The same idea holds for more complicated scenarios involving more than two people and more than two goods. If people in a society decide to specialize, and make a lot of what they are good at making, and then trade some of the thing that they make for other things they want, then both they and the society they are part of will be better off. Or, as I will say a little later on, specialization and trade generates wealth for society.

This is perhaps not hard to understand. We all specialize in something and sell it and use the proceeds of that sale to buy other things. A university professor specializes in teaching students and generating research. The university pays the professor for this, and with his wages he buys food, housing, transportation, clothing, leisure, and many other things. He is better off doing this than trying to make his own food, build his own house and manufacture his own car. A construction company might build a hundred houses a year, which is more than the owners of the company need. So, they sell some of those houses to buy the other things they need to live. This is how our society is organized.

As a society, we have much more wealth because we arrange our societies this way. Without trade (that is, buying and selling things), we would each have to be a fully self-sufficient unit, and each of us would have much less in such a world. We do not trade because we like each other or even care about each other - we usually don't even know the people we are trading with - but we do so because it is in our own best interest. This curious fact - a society of people, each acting in their own best interest (or out of selfish motives), leads to an increase in the wealth of society as a whole - was first written down and expounded upon by Adam Smith, the author of a book called The Wealth of Nations, which was written in 1776 and was the founding text of modern economic thought. We'll talk a bit more about Smith later.

Now, given this simple example as an introduction, we can move on to start talking about economics in a bit more of a formal and structured manner.