(41)
a.h EJ s 7Th ) dX.s J s
x{(-rv,X)~h(-rv,X)'}a = -a.a.h
] J
and the general wealth effect vanishes if and only if a.
= o.
J
Thus we have.
Proposition 5.
Under spanning and given that
n.
< O, a necessary and sufficientcon-J
dition for maximization of excess demand for firm j's shares to be locally consistent with the shareholders' interests is that dX. is
]
contained in the row space of X other than row j .
Under spanning all shareholders will agree in the ex post sense on the desirability of a firm' s invest:nent plan and if they perceive that implicit prices do not change they will all support stock value maximization. From proposition 5 it follows, .however, that actual value maximization will not be in the shareholders' interests unless the marginal return pattern asso-ciated with the investment plan can be obtained as a linear combination of existing shares in the market not involving the shares of the firm contem-plating investment. In that case firm j's monopoly power in the stock
market washes out as there exists a perfect substitute in the market for the marginal return pattern dXj consisting of a linear combination of shares in firms other than firm j.
VI. Concluding remarks.
In the presene paper we have explored the efficiency implications of value-related investment criteria for decentralized investment decisions under technological uncertainty and the general conclusion is negative in the sense that except for some special cases, the market allocation of investment effected through decentralized and incomplete capital markets is likely to be inefficient. This is so because investment decisions
I
under uncertainty will generally have external effects for which there do not exist well-defined stock market prices and hence, there does not in the general case exist any clear or well-defined definition of competi-tive behaviour based on observable market characteristics in which case the
competitive benchmark with respect to investments does not seem to be meaningful. Indeed, in the general case the choice of a Pareto efficient
investment plan in a given firm requires explicit knowledge of consumers' preferences as one would expect in cases where firms' production plans have external effects not fully reflected through competitive profits at market prices.
/
Under certain conditions as to market structure (complete set of markets) or on the stochastic technologies (spanning) the external effects asso-ciated with investment under uncertainty will vanish in which case all welfare-relevant consequences of an investment plan will be fully priced in the stock market and changes in stock market values at given stock prices will capture the social value of the plan. On the other hand, if preferences satisfy the separation property and shareholders have identical beliefs, all shareholders will evaluate the external effects associated with any given investment plan in the same way, and hence they will all agree on the social value of any given investment plan and the Pareto
efficient plan could be chosen by a unanimous vote. Alternatively, the firm could choose the Pareto efficient plan through relying on.the preferences of an arbitrary shareholder and formally the efficient plan would maximize
the firm's stock market value of initial interests at the shareholder's given individual implicit prices for st·ate-contingent income (being the same for all shareholders in that case).
It follows triviallY that when decentralized value maximization by competi-tive firms is well-defined and leads to Pareto efficiency, value maximizing investment decisions will be unanimously approved by all shareholders. The converse conclusion does, however, not follow, that is a Pareto efficient allocation may not be obtained through the decentralized market mechanism with market value maximizing firms as there will in general be externalities
associated with firms' investments ~n incomplete markets. In such cases the market will not provide adequate price and value signals for shareholders to compute the social value of investment and hence shareholders may not unani-mously support Pareto efficient investment plans because of lack of relevant
information except for the case with preferences exhibiting separation and with identical beliefs in which all will agree.
Most of the examples given inthe literature assume implicitly away the pr~ce information problem in that they are within the mean-variance context and hence consumers' preferences exhibit separation. It is therefore argued here that
the controversy between value maximization and shareholders' unanimity is in these cases caused by an inadequate specification of competitive behaviour in incomplete markets.
In the first place the conventional value maximizing rule as specified by i.'a. Stiglitz (1972a), Jensen
&
Long (1972) and Fama (1972) defines price-taking with respect to the "wrong" prices as it implies a downward sloped demmd schedule for shares which are the true objects of choice ~n incomplete markets. It is therefore not surprising that the market outcome in that case turns out to be inefficient and in such cases value maximization would clearly not be in the interest of all shareholders.Second, one must distinguish between value maximization in the perceived and in the actual sense. True competitive behaviour requires that producers do not take into account any relationships between prices and their own production decisions, i.e. , perceived value maximization. This is a well-known prerequisite for efficiency of market behaviour in general and should not be mixed up with the empirical question of whether or not firms are able to influence prices in the stock markets and do take this into account.
Some authors1) have stressed the fact that in the case firms' return patterns are linearly independent, each firm would have a monopoly on its own return pattern and one would expect this to affect firms' market behaviour. It has been verified here, however, that in case of spanning any monopoly power firm j may h~ve will vanish if the ·returns on new
investment is contained in the space spanned by the returns of firms other than j. In case of separation only aggregate returns in each state would matter for implicit prices so that a firm's monopoly power would in that case depend on its marginal contribution to aggregate returns in each state'. In all other cases firms' investment under uncertainty generates external effects pointing to likely inefficiency of decentralized market behaviour. As the market in such cases will not provide adequate informa-tion for a proper evaluainforma-tion of the æc ial desirabilityoffirms ' investment plans, there does insu:hcases not exist any market alternative for aggregation of consumer preferences. In this respect, the allocative problems caused by the external effects of investment are in a fundamental way different from those caused by firms' ability to affect market prices which is clearly in the nature of pecuniary external effects.
1) See ~.a. Mossin (1973).