# A4 Taxes and Economic Growth

## A4.1 The Constrained Economy

We now consider the effect of taxes on capital accumulation in the bequest- constrained economy of M = 0. When taxes are incorporated, Eq. (5.A19) may be rewritten as

Considering Eq. (5.A8.1), it is easy to find that the right-hand side of (5.A19^{0}) increases with k, while the left-hand side of (5.A19^{0}) decreases with k. Hence, as in Sect. A3.3, the steady-state physical capital/human capital ratio *к* is uniquely determined.

In this instance, Eq. (5.A22) may be rewritten as

An increase in the tax on life cycle capital income (an increase in the interest income tax), t, reduces *к* and hence depresses the growth rate.

However, the effect of an increase in the tax on income from human capital (an increase in the wage income tax), 0_{B}, on the growth rate is ambiguous. It directly reduces the growth rate, while it indirectly raises the growth rate by increasing *к* and h. Namely, an increase in the wage income tax raises the physical capital/human capital ratio, and hence increases h. If this indirect effect predominates, an increase in the wage income tax raises the growth rate.

Finally, let us consider how to attain the first best solution by using capital taxes. The optimal levels of т and 0_{B} are given respectively by

From Eq. (5.A28), the optimal level of 0_{B} is negative so long as 5 > 0. Further, in order to attain к* = к, an additional lump sum intergenerational transfer from the young to the old, such as debt issuance or unfunded social security, is also needed. Such a policy can substitute for negative bequests.