This paper extends the fundamental theorem of share (or capital) valuation under conditions of certainty and purely competitive markets, to allow for the distinction between capital gains and income in the taxation of personal income. The objective is to develop the theorem for the tax case in a form general enough to allow for corporations both currently and not currently paying a dividend. However, the general derivation is sufficiently tedious to warrant a presentation which begins with less general cases. Accordingly, we will first develop the share valuation equation for a continuous discount version of the taxless case for corporations either paying or not paying a dividend. Then we turn to the effect of income and capital gains taxes for corporations currently paying a dividend; and finally the more general case. The derivations will be simplified by assuming a constant rate of interest over time, but all the theorems can be extended to deal with foreseen changes in interest over time.

This paper is not directed to the question of whether the Treasury should or should not practice in the public sector what the Clayton Act prohibits in the private sector. The paper is concerned exclusively with the theoretical question of whether the Treasury would necessarily receive higher prices by employing price discrimination than it could get by selling the issues at a single price. From a theory of bidding under uncertainty, which seems to apply naturally to the Treasury auction, it will be shown that buyers may be expected to enter lower bids under price discrimination than they would for a simulated competitive auction. If this analysis is accepted, it suggests that the Treasury may actually get less revenue from a given bill offering under price discrimination than under a competitive auction.