This paper shows that if the difference of two positive semidefinite matrices is positive semidefinite then the difference of their generalized inverses is negative semidefinite. It uses this to compare comparative static behaviour over feasible sets whose distance functions have Hessians with a positive semidefinite difference. It then interprets this condition in terms of various ideas of the relative convexity of the two sets and relates it to the Le Chatelier principle.

[The downside risk in a leveraged stock position can be eliminated by using stop-loss orders. The upside potential of such a position can be captured using contingent buy orders. The terminal payoff to this stop-loss start-gain strategy is identical to that of a call option, but the strategy costs less initially. This article resolves this paradox by showing that the strategy is not self-financing for continuous stock-price processes of unbounded variation. The resolution of the paradox leads to a new decomposition of an option's price into its intrinsic and time value. When the stock price follows geometric Brownian motion, this decomposition is proven to be mathematically equivalent to the Black-Scholes (1973) formula.]

[Measurement errors may have reduced the usefulness of current-cost and replacement-cost data. Under the provisions of Accounting Series Release No. 190 (ASR 190), replacement-cost valuations of plant and equipment (and related depreciation) often include the cost of technological advances and often these advances would reduce operating costs below the level reported by historical cost. As a result, when replacement-cost depreciation is substituted for historical-cost depreciation, the cost of doing business includes the high capital cost of the advanced technology as well as the high operating costs of the older technology in use, which creates measurement errors. ASR 190 was criticized because the reported depreciation amounts are not suitable for calculating income. Although Statement of Financial Accounting Standards No. 33 (FAS 33) includes provisions to remedy this problem, they may not have been effective because relatively few firms have reduced related depreciation expense to adjust for the present value of operating-cost savings. Moreover, numerous firms have relied on price indexes, which are not known to fully reflect technological changes. Therefore, the question arises as to whether current-cost data have substantially less measurement errors than replacement cost-data as a result of ignoring the effects of technological change. Analysis of a sample of 75 firms that reported under both methods for 1979 shows that current-cost depreciation is substantially smaller than replacement-cost depreciation for most firms. This finding suggests the presence of a smaller measurement error from technological change in the current-cost data compared with replacement-cost data. Nevertheless, additional analyses indicate the existence of measurement error in current-cost data also. First, an error component is common to about 25 percent of the sample firms that reported almost identical depreciation amounts under current cost and replacement cost. Second, the excess of replacement-cost depreciation over current-cost depreciation is not in proportion with the amount of potential operating-cost savings described in narrative disclosures accompanying the replacement-cost data. If these narrative disclosures are accurate, this divergence suggests incomplete adjustments of current-cost data for this type of technological change. Third, potential tax incentives may have influenced the measurement of current cost. Voluntary disclosure of effective tax rates on a current-cost basis is associated with the choice of measurement method (greater use of indexation). Moreover, current-cost and replacement-cost depreciation are relatively more similar for firms disclosing effective tax rates than for nondisclosing firms (suggesting smaller adjustments for technological change in current-cost data, which results in higher current-cost tax rates).]

It is often argued that the same expenditures on military procurement would produce a more effective defense if larger numbers of less sophisticated (and thus cheaper) weapons were purchased. This paper shows that such a result can occur even if the military derives no private consumption value from technically sophisticated weapons. Rather the organization of the decision-making process itself can produce this result. This suggests some possible solutions through organizing decision making in a different fashion.

The phenomenal growth in our public deficits over the past twenty years is a matter of public and professional concern (see Symposium, 1989). While this concern may indeed be well founded (particularly given current deficit levels), public deficits are not always bad. Certainly in times of deep recessions, short-term deficit financing can stimulate aggregate demand, increase national income, and reduce unemployment in a Keynesian fashion (see Richard Startz, 1989). Second, long-term deficit financing may be needed to sustain a long-term path of optimal consumption (see Peter Diamond, 1965). Third, public deficits (including pay-as-yougo Social Security) can offer welfare gains for significant subsets of consumers who have been liquidity constrained (R. Glenn Hubbard and Kenneth Judd, 1986), who have been unable to purchase indexed private annuities (Alan Blinder, 1988), or who have been unable to sufficiently diversify their investment portfolios away from human capital (Robert Merton, 1983). Finally, Robert Barro (1979) has argued that public deficits may be an important policy instrument to insure intertemporal welfare maximization when public expenditures are stochastic and public taxes are economically inefficient; taxes can be smoothed to reduce the lifetime excess burden of public financing. The concern today is not that we have deficits, but rather that we may be overdoing a good thing. If this is the issue, then we need to ask: Why, and what can be done about it? This is my agenda here. I. The Political Economy of Recent Deficits

It is often argued that the same expenditures on military procurement would produce a more effective defense if larger numbers of less sophisticated (and thus cheaper) weapons were purchased. This paper shows that such a result can occur even if the military derives no private consumption value from technically sophisticated weapons. Rather, the organization of the decision-making process itself can produce this result. This suggests some possible solutions through organizing decision-making in a different fashion.