Why do we need a capital gains tax?

If we start from the premise that the Government has the right to extract a proportion of GDP as the price we are all required to pay for maintaining the state then value creation should be subject to tax. The problem with taxing wealth creation is that individuals are very skilled at avoiding any tax liability. As Oliver Williamson remarked people are characterised by opportunism and guile and that is nowhere better exemplified than in the area of taxation.

In general terms value creation is driven by the proportion of social reinvestment. Value extracted as income is caught under the various income taxes whilst value reinvested is caught both by capital gains tax and by income tax on future value withdrawn. Without CGT, government would recover its share of social value created through income tax but only after a significant time delay. CGT from the state's perspective would be neutral in its effect only if it just compensates for the time delay in receiving 'its share' of current value creation lost through reinvestment.

If the rate of return on reinvestment is the same as the social time preference rate (the discount rate) then taxing capital gains at exactly the same rate as income leads to a neutral outcome as far as government is concerned. A lower rate of CGT will distort towards reinvestment, a higher rate towards consumption. But how do things change if the rate on reinvestment is less than the discount rate (which it will be unless 100% of value generated is reinvested)? Any bloggees fancy working out the neutral CGT rate assuming GDP growth of 5% and a discount rate of 8%?