“A Note on the Joint Occurrence of Insurance and Gambling,” Macroeconomic Dynamics, Vol. 1, No. 1, February 2008. Download PDF.
This is a (very) old paper of mine that some people have wanted to see lately, but was never published. So I got a spanking new electronic version of it made up along with a very nice new version of the graph (thanks Anderson!) to replace the hand drawn one in the original.
Basically, it uses indivisibilities in the consumption set to generate a Friedman and Savage style indirect utility function over wealth, thereby rationalizing gambling even in the presence of (usually) risk averse agents. Basically, agents 'jump across' the indivisibility (i.e., retire, buy a vacation home, etc.) when they win the lottery. If they are very poor, or very rich they do not gamble.
There are also two examples that show that this intuition can break down when time is continuous, or there are a continuum of qualities of the indivisible good. (These are the examples people have been interested in lately.)
I never did anything with this note because it turns out that the basic idea had already appeared in print but it had become lost. That citation is:
"Why do People Buy Lottery Tickets? Choices Involving Risk and the Indivisibility of Expenditure," Ng Yew Kwang, Journal of Political Economy , Vol. 73, No. 5 (Oct., 1965), pp. 530-535.