@ AJ and Andris,
I think that’s what Friedman was getting at when he said “I think that once one takes seriously both how complicated a utility function and how complicated a production function can be, you will discover that if you limit yourself to a priori argument you can’t do much, if any, economics.”
I think nirgrahamUK and DD5 explained the Austrian way of looking at things very well in that thread. We Austrians are defining “a good” in way that is entirely subjective, and the problem comes when we point to an objective “good” in the real world and try to use our theories to explain it’s price.
If we start off being entirely subjective, there is no relationship at all between “4 tyres” and “1 tyre”. There are certain ends (like a tyre swing) that can be achieved using 1 unit of the good “1 tyre” and there are certain ends (like a car) that can be achieved using 1 unit of the good “4 tyres”. That there is an objective, physical relationship between these two goods does not matter to the subjectivist. The law of DMU applies to both goods separately. We can construct a demand curve for units of the good “1 tyre” and a separate demand curve for units of the good “4 tyres”.
The physical relationship between these two goods means that their demand curves are very closely related. I think the proper way of thinking about it is to consider that it is virtually costless to “switch” or “arbitrage” between the two goods, or to “produce” the one good using the other. 4 units of “1 tyre” can be used as a means to “produce” 1 unit of “4 tyres”. And 1 unit of “4 tyres” can be used as a means to “produce” 4 units of “1 tyre”. Both of these production processes are so cheap that any price disparity between the price of 4 units of “1 tyre” and the price of 1 unit of “4 tyres” will be closed very quickly. Because of this fact, we generally combine the demand curve for units of “1 tyre” and units of “4 tyres” into one demand curve for “tyres”. This simplification causes problems when we try to apply the law of DMU to the combined good, rather than each good separately.
The reason I use the word “arbitrage” above is because it’s really no different to ordinary arbitrage. We talk about the demand curve for “gold”, or price of “gold”, but this a simplification because actually each individual gold seller faces a different demand curve. The reason we simplify is because it is very easy to arbitrage between “gold in London” and “gold in Edinburgh”, so we don’t bother breaking it down that far and just talk about the price of “gold” in general.