Pareto-improving Consumption Tax When the Return from Capital is idyosyncratic and (Optimal or non-Optimal) Capital Income Tax is available

In the standard multi-period model, the consumption tax and the wage tax are equivalent. When a capital market is incomplete, such that the rate of return from capital is idiosyncratic, the consumption tax, in contrast to the wage tax, can play a role in risk-sharing. However, risk-sharing may disappear if the government applies a linear or non-linear capital income tax, because the source of risk is the return from capital. The present study shows that a consumption tax, when instituted in the presence of a wage tax, increases welfare when the capital market is incomplete, even if the government applies a non-linear capital income tax for risk-sharing and subsidizes investments.