Having more fun than the government allows

As you know, I've started posting some of my letters on the Alexandria blog. I am also commenting on this blog quite often. As you may imagine my progressive thinking is not necessarily appreciated by everyone there, but it will pass - I am sure I will charm everyone there with my polite manners and diplomatic choice of words. In the meantime, I've posted a new letter there, and I have a feelling some of the people will enjoy reading it...

_________________________________________________________________


I've been having an interesting discussion with comrade Siarlys Jenkins, and he made the following peculiar observation:

They [bloody capitalists] don’t hire as a public service, they hire because they think they can make money out of hiring you. As long as the taxation rate is below 100%, they’ll get to keep more of that profit than if they didn’t hire you at all.

Our co-blogger was advocating a drastic increase in the taxation of profit (as long as the rate is below 100%, the capitalists will keep hiring folks and developing their business, right?), and he believes that it's obscene when anyone earns more than 1 million dollars. It was never explained why 1 million dollars was the cut-off sum (for example an afghan sheep herder may decide that making more than 50 thousand dollars is obscene and should be taken away to feed the poor in Kenya) - but that's a separate issue - and I suggest you read an article on my blog that explores this particular question. But the idea of maximizing the tax rate on profit intrigued me - I cannot deny that. In order to demonstrate the fallacy of Siarlys thinking, I composed a simple arithmetic problem. I am curious how many of the intellectuals on the Alexandria blog would be willing to spend the time to solve it. I would also appreciate people commenting on the result - why do they think the tax rate at which it becomes uneconomical to invest is lower than 100%.


I am thinking about investing $100. It’s a one time deal. If everything goes right (80% chance), I will profit $50 from it. There is a 20% chance that everything will go wrong, and my entire investment will be lost. At what tax rate for the profit will it become uneconomical for me to make this investment? Discuss the results.


I believe this little problem will be useful for two reasons. Firstly, it would allow the intellectual community of this blog to entertain themselves with a trivial mathematical problem (and who of us does not enjoy reading math books from time to time?). Secondly, this problem illustrates the complexity of the free market economy, and some ill-effects of taxation which may not be apparent at the first glance.