So, let's write down the firm's problem again, assuming a constant real interest rate

*r*, which the firm's shareholders face (an important assumption - I'm neglecting taxes affecting the sharelholders). We'll assume that dividends are paid period-by-period to the firm's shareholders, with the firm maximizing the present value of dividends: Here,

*K*is the capital stock,

*N*is the labor input,

*w*is the wage rate,

*b*is the firm's debt, and

*d*is the depreciation rate. The firm's debt comes due in one period. Net proceeds for the firm in the current period consist of output minus the wage bill plus new debt issued, minus interest and principal on the debt issued in the previous period, minus investment, minus corporate taxes. The corporate tax rate

*t*applies to output minus the wage bill, minus the interest payments on the debt, minus depreciation.

If the firm were to fund investment out of retained earnings (provided this does not violate a nonnegativity constraint) then a reduction in the corporate tax rate will indeed raise the after-tax marginal net payoff to investing. Alternatively, suppose that the firm always funds new investment by issuing debt, then pays the interest on the debt, retires debt as capital depreciates, and otherwise rolls the debt over. This implies that the firm's outstanding debt is always backed one-for-one by the firm's capital, or Then, we can rewrite the first equation as So, the firm's choice of labor input in each period, and its choice of capital in periods 1,2,3,... (equivalent to choosing investment) is independent of the tax rate

*t*. Essentially, debt financing of investment permits full expensing of the investment expenditure - indirectly, through expensing of interest on the debt and depreciation.

Caveats:

1. We need to worry about how the household is taxed, which in this formulation determines what the objective function is for the firm.

2. To do a proper job here, we need to determine the optimal financial structure for the firm.

This is potentially quite complicated (not blog material), though I'm sure someone has addressed related problems in the taxation literature. To do the problem justice, we need a complete general equilibrium model. That said,

1. There's no presumption that the corporate tax rate reduction is going to matter much for intensive-margin decisions of the firm - decisions about labor input and investment.

2. Where the change in the corporate tax rate should matter is for entry decisions - here we need to start worrying about nonconvexities - e.g. fixed costs of entry. But some entry, relating to the treatment of pass-throughs, would just be a renaming of the productive unit - call yourself a business and you can be taxed at a lower rate. As well, firms may choose to relocate from other countries to the U.S., though as I mentioned in my previous post, those other countries won't give up without at fight.

3. There's a clear redistributive effect, as I mentioned in my previous post. Owners of stocks will benefit, and they tend to be richer people. Long-term, government transfers and expenditures on goods and services have to fall, and the burden of those reductions will be borne by the relatively poor.

4. If the Republican Congress actually wanted to increase investment spending, there are straightforward ways to do this through the tax code - an investment tax credit, for example.