<|endoftext|> than you at both cooking and mowing, and that if I were there would be no way in which I could benefit from trading with you.
This seems to make sense, but it is wrong--as a simple example will show. Suppose I can cook a meal in 15 minutes and mow a lawn in 1/2 hour. It takes you 1/2 hour to cook a meal and 2 hours to mow a lawn. I am better at everything; what can you offer me to trade?
Just as before, you offer to cook my meals in exchange for my mowing your lawn. Before the trade, you spent 1-1/2 hours cooking 3 meals and 2 hours mowing your lawn, for a total of 3-1/2 hours. After the trade, you spend 3 hours cooking meals for both of us. You are better off by 1/2 hour. What about me?
Before the trade, I spent 45 minutes per day cooking and 1/2 hour mowing, for a total of 1-1/4 hours. After the trade, I spend 1 hour per day mowing both lawns, for a total of 1 hour. I am better off too! How can this be? How can it pay me to hire you to do something I can do better?
The answer is that the relation between cost to me and cost to you in time has nothing to do with whether we can gain by trade; time is not what we are trading. The relevant relation is between my cost of mowing a lawn and yours in terms of meals cooked--our opportunity costs. We are, after all, trading mowed lawns for meals, not for time.
In the first example I gave, the opportunity cost to me of mowing a lawn was 2 meals, since mowing 1 lawn took the time in which I could have made 2 meals. The opportunity cost to you of mowing a lawn was 8 meals. Since lawn mowing cost much more to you (in terms of meals) than to me, it was natural for you to buy lawn mowing from me and pay with meals.
A different way of describing the same situation is to say that the cost to me of producing a meal was 1/2 lawn and the cost to you was 1/8 lawn. Since meals cost you much less than they cost me (in terms of lawns), it was natural for me to buy meals from you, using lawn mowing to pay you. These are two descriptions of the same transaction; when we trade lawn mowing for meal cooking, we can describe it as buying lawns with meals or meals with lawns, according to whose side we are looking at it from.
Since a lawn costs you 8 meals, you are willing to buy lawn mowing for any price less than 8 meals per lawn--it is cheaper than producing it yourself. Since it costs me 2 meals, I am willing to sell for any price higher than 2. Obviously there is a wide range of prices at which we can both benefit--any price of more than 2 meals per lawn and less than 8 will do.
Now consider the second example, where I can cook a meal in 15 minutes and mow a lawn in 30, while you take 30 minutes to cook a meal and 2 hours to mow a lawn. The cost of mowing a lawn to me is 2 meals; the cost of mowing a lawn to you is 4 meals. I benefit by trading lawns for meals as long as I get more than 2 meals per lawn; you benefit by trading meals for lawns as long as you pay fewer than 4 meals per lawn. Again, there is room for both of us to benefit by trade.
Once we realize that the relevant cost of producing one good is measured in terms of other goods, it becomes clear that I cannot be better than you at everything. If I am better at producing lawns (in terms of meals), then I must be worse at producing meals (in terms of lawns). If this is not obvious when put into words, consider it algebraically.
Let L be the time it takes me to mow a lawn and L' the time it takes you. Let M be the time it takes me to cook a meal and M' the time it takes you. The cost to me of mowing a lawn (in terms of meals) is L/M; if a lawn takes 30 minutes and a meal 15, then a lawn takes the time in which I could produce 2 meals. The cost to you is L'/M'. But the cost to me of a meal in terms of lawns is, by the same argument, M/L; the cost to you is M'/L'. If L/M > L'/M' then M'/L' > M/L. If you are better than I am at mowing a lawn, I must be better than you at cooking a meal.