Abstract
The optimality of the long-run capital-income tax rate is revisited in a simple neoclassical growth model with credit frictions. Firms pay their factors of production in advance, which requires borrowing at the beginning of the period. Borrowing, in turn, is constrained by the value of collateral that they own at the beginning of the period, leading to inefficiently low amounts of capital and labor. In this environment, the optimal capital-income tax in the steady state is non zero. Specifically, the quantitative analyses show that the capital-income tax is negative and, therefore, the distortions stemming from the credit friction are offset by subsidizing capital. However, when the government cannot distinguish between capital-income and profits, the capital-income tax is positive as the government levies the same tax rate on both sources of income. These results stand in contrast to the celebrated result of zero capital-income taxation of Judd (Judd, K. 1985. “Redistributive Taxation in a Simple Perfect Foresight Model.” Journal of Public Economics 28: 59–83.) and Chamley (Chamley, C. 1986. “Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives.” Econometrica 54: 607–622.).
Acknowledgments
I am grateful to the editor and to an anonymous referee for very helpful comments and suggestions.
Appendix
A. The firm’s problem
At the beginning of period t, the firm obtains a loan
subject to:
and:
Letting υt and γt be the Lagrange multipliers on the constraints (A.2) and (A.3), respectively, the optimality condition with respect to
Similarly, the first order conditions with respect to lt and kt yield:
Recalling that
and, therefore, the two Lagrange multipliers are equal. By renaming the Lagrange multiplier as μt, we get conditions (11)–(12) in the text.
Alternatively, conditions (A.2) and (A.3) can be combined to get:
which is condition (10) in the text.
Substituting
which is condition (9) in the text. Therefore, the optimization problem of the firm is to maximize (A.9) subject to (A.8). Letting μt be the Lagrange multiplier on (A.8), the choices of labor and capital yield conditions (11) and (12) in the text.
B. Efficient allocations
The problem of the social planner is to maximize:
subject to the sequence of resource constraints:
and the market clearing condition of real estate:
Letting ηt be the Lagrange multiplier associated with condition (B.2), the first-order conditions with respect to ct and kt+1, respectively, read:
Combining these two conditions gives condition (17) in the text.
C. The present-value implementability constraint
I show here the derivation of the PVIC for the Ramsey problem. Recalling that
By introducing
Recall that, from the solution to the households’ problem, we have:
Substituting (C.3) in the first term of (C.2), (C.4) in the eighth term of (C.2), (C.5) in the seventh term of (C.2) and (C.6) in the last term of (C.2) yield:
Combining the second and seventh terms of (C.7) yields:
Combining the fifth and eighth terms of (C.7) gives:
Combining the fourth and last terms of (C.7) yields:
Also, the first term of (C.7) can be written as:
Finally, substituting (C.8)–(C.11) into (C.7) and re-arranging give the PVIC (condition (18) in the text):
with
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