Now, assume for the second that the contest attracts just one contestant. Even after spending a few months digging, he would have to continue his work, because he would not know if there were someone else at some other of my estates competiting. So this guy digs and fills holes, straight, for 10 years. He gets the million.
Pretty clearly, the whole thing has wasted a great deal. If the guy had worked for the same pay, at a real job that served people, he would have created a million dollars of wealth (or perhaps, just $500000, say, but clearly a lot). Instead, he spent the time at laborious, but useless, digging. Total waste. (Incidentally, a clear demonstration that the labor theory of value is junk and always will be.)
Now imagine that there were many volunteers, each at a different estate thinking, but not knowing, that he would win the prize. If there are ten of then, my contest could waste up to $10M! With even more contestants, even more could be wasted. In fact, if I could somehow get everyone in society involved (and keep them all ignorant of each other's progress), I could waste the entire GNP, with only my tiny million as the bait!
This phenomenon - the expenditure of scarce resources to capture a pure transfer - is called by economists rent seeking. (The term is perhaps somewhat unfortunate in using "rent" in a special way; it's not related to "rent" as we normally think of it, as payment for use of a resource owned by someone else.) The first analysis of the problem was done in 1967 by Gordon Tullock. The term itself was coined by Anne Kreuger, in a classic article "The Political Economy of the Rent-Seeking Society," (1974). Quoting Tullock in his introduction to rent seeking:
Kreuger's paper focused attention on third world mixed economies in which government intervention was extensive. She provided quantitative estimates of the social losses imposed upon the economies of India and Turkey by rent-seeking for import licences. According to her estimates, such losses amounted in 1964 to 7.3 per cent of the national income of India and to a staggering 15 per cent of the national income of Turkey. Numbers of this magnitude were sufficient to turn the heads of even the most left-leaning of the world's development economists.15% is staggering indeed. As my silly imaginery contest shows, private rent seeking problems are possible. However, almost all serious rent seeking struggles in the real world are creations of governments, or to be more specific, the state. Read Tullock's intro (it's short) for a few more good examples.
The reason I bring this up is I want to use the concept on this blog. So consider yourself warned, and I hope, educated.