Saturday, May 06, 2006

The Benefits of Trade, Part I

HT, Sawdust from above link.
Warren Buffett and Bill Gates have billions of dollars. Last year I took a piece of vacant land and built a cabin on it. I worked hard and put in some sweat equity and now my cabin is worth a lot more than I paid for it. I created value by using my capital both financial and physical.
Here is my question. How did the vast wealth of Warren Buffet and Bill Gates stop me from doing what I wanted to do and making a profit?
So called "hoarded wealth" is only called that by those who don't understand what wealth is. Wealth is the end result of creating value. People who inherit wealth benefit from the value created by their families or ancestors. The ability to create value exists in all of us, regardless of the wealth that others have created for themselves.

Which had me thinking of the strong liberal meme of Zero Sum Games:
Zero-sum describes a situation in which a participant's gain or loss is exactly balanced by the losses or gains of the other participant(s). It is so named because when the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Chess is an example of a zero-sum game - it is impossible for both players to win. Zero-sum is a special case of a more general constant sum where the benefits and losses to all players sum to the same value. Cutting a cake is zero- or constant-sum because taking a larger piece reduces the amount of cake available for others. Situations where participants can all gain or suffer together, such as a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, are referred to as non-zero-sum.

And this lead me to think back to a forum (About.com Economics) I visited that posed the following question:
Let's say that I need to cook 3 meals a day and mow my lawn once, and you do too. It takes me 3 hours to mow my lawn and 6 hours to cook one meal. It takes you 2 hours to mow a lawn and 1 hour to cook a meal. So, if we both mow our own lawns and cook our own meals, it takes me 21 hours and it takes you 5 hours. But, it look like you have a comparative advantage in cooking meals...

And costs per hour to complete tasks:
__Lawn | Meals

You(1)--- 2 --- 1

Me(2) -- 3 --- 6

Now the question is: can they trade the chores and benefit both parties at the same time? The writer of this question then falls into the trap that when the trade occurs, that both will specialize 100% in the relatively more efficient task...
If you specialized in cooking all our meals and I specialized in mowing both our lawns, then I would be better off (now only spending 6 hours mowing), but you will be worse off because now you spend 6 hours cooking meals.

But before we step to the conclusion of complete specialization let us first break down what each individual is willing to trade for and still get a benefit from trade.

Some assumptions that I will be using is that both tasks are both a negative utility (something you don't want to do) at the same level and thus the goal is to minimize amount of time doing labor. And secondly no transaction costs. Now You(person 1) is willing to trade 2 meals for any one mowing and still be the same off. Anything less than that trade off will make 1 better off. And Me(person 2) is willing to 2 lawns for 1 meal and be at the same level of utility.

To make the trade easier I will come to the conclusion that they negotiate a price of one mowing for one meal. So #2 will mow both lawns and #1 will do her three meals and do one meal for #2 and thus #2 will still have to fix 2 meals.
So what are the results:
#1 person (3+1) meals*1 +(0)lawn*2=4
So originally 5 hours and #1 saved 1 hour.
#2 person (2) meals*6 + (1+1)lawn*3=18
So originally 21 hours and #2 saved 3 hours.
And in conclusion both benefited from trade and society as a whole also got 4 more hours to spend with their kids or enjoy life more, with no one being worse off in the process!!!


Links:
Simple Trade

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