# Corporate Tax and Borrowing Funds

In reality, only interest payments on borrowing funds are subtracted from the tax base. Thus, the rental cost of capital is not always subtracted. In this regard, corporate tax could affect investment.

The optimal condition of investment means that investment is conducted only if the after-tax marginal profit is greater than (or equal to) the rental cost of capital. The after-tax marginal profit is given as (1 — t_{I})pF_{K}. Here, F_{K} is the marginal product of capital. Under normal corporate tax law, interest payments on bonds are not taxed. Thus, the rental cost in a bond-financed investment case is (1 — t_{I})r. Since the term (1 — t_{I}) appears in both sides of the condition, the optimal condition is the same as for t_{I} = 0.

In other words, with regard to borrowing funds, rK is subtracted from the tax base. Then, after-tax profit is given as Eq. (8.15) and the optimal conditions are still given as Eqs. (8.16) and (8.17).

# Corporate Tax and Retained Earnings

With regard to investments financed by retained earnings, the interest payments on borrowing funds do not exist. Hence, investment does not affect the tax base and the rental cost of capital is not affected by the tax. Thus, we may compare (1 — t_{I})pF_{K }and r. It follows that t_{I} affects investment. For example, an increase in t_{I} reduces after-tax marginal profit, depressing investment. Alternatively, even with regard to bond finance, if interest payments are not tax-free, the rental cost of capital remains at r. Then, an increase in t_{I} depresses investment.

Namely, in the case of retained earnings, rK is not subtracted from the tax base. In place of Eq. (8.15), we now have as after-tax profit

Hence, the optima1 conditions are rewritten as

t_{I} only appears in Eq. (8.16^{0}). An increase in t_{I} depresses K, while it does not affect the demand for L.

Figure 8.6 explains the effect of corporate income tax on investment. The vertical axis denotes the interest rate r and the (after-tax) marginal product of capital (1 — tI)pFK. The horizontal axis denotes capital. The optimal point is given by the intersection of the (after-tax) marginal product curve and the interest rate line.

**Fig. 8.6 ****The effect of corporate income tax**

An increase in tj moves the (1 — tj)pF_{k} curve downward from AA to A'*A'.* Thus, the optimal point moves from E to E'. The optimal capital stock declines from B to B', depressing investment.