Effects of a capital gains tax on asset pricing

I extend and generalize the work of Kruschwitz and Löffler (BuR-Business Research 2(2):171-178, 2009). I find that, with a zero risk-free rate, the implicit price of capital gains tax payments is zero. I provide conditions in stochastic discount factor language when a capital gains tax has no effect on asset prices for the case of a zero risk-free rate. A sufficient condition for price equality with a zero risk-fee rate is that agents consume the same in any state with and without taxes. Equilibria exist that guarantee equal consumptions, and they imply the same portfolio rules that Kruschwitz and Löffler (BuR-Business Research 2(2):171-178, 2009) find for the CAPM. Furthermore, for an exogenous non-zero risk-free rate, I show that exponential utility with multivariate normal payoffs, as well as linear marginal utility leave prices unchanged. Equilibrium prices are independent of capital gains taxes in those cases. However, total wealth of agents is different between the tax and the no-tax economy.