The Market System as an Efficient Mechanism for Information

Most decision-making situations involve the choice of one among several alternative actions. The alternative actions and their corresponding payoffs are usually known to the decision-maker in advance. A prospective investor choosing

one investment from several alternative investment opportunities, a store owner determining how many of a certain type of commodity to stock, and a company executive making capital-budgeting decisions are some examples of a business

decision maker selecting from a multitude of alternatives. The decision maker however, does not know which alternative will be best in each case, unless he/she

also knows with certainty the values of the economic variables that affect profit.

These economic variables are referred to, in decision analysis, as states of nature

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as they represent different events that may occur, over which the decision maker has no control.

The states of nature in decision problems are generally denoted by si (i = 1, 2, 3…

k), where k is the number of or different states of nature in a given business and

economic environment. It is assumed here that the states of nature are mutually exclusive, so that no two states can be in effect at the same time, and collectively

exhaustive, so that all possible states are included within the decision analysis.

The alternatives available to the decision maker are denoted by ai (i = 1, 2, 3, …,

n), where n is the number of available alternatives. It is also generally assumed that the alternatives constitute a mutually exclusive, collectively exhaustive set.

When the state of nature, si, whether known or unknown, has no influence on the outcomes of given alternatives, we say that the decision maker is operating under certainty. Otherwise, he/she is operating under uncertainty.

Decision making under certainty appears to be simpler than that under uncertainty.

Under certainty, the decision maker simply appraises the outcome of each

alternative and selects the one that best meets his/her objective. If the number of alternatives is very high however, even in the absence of uncertainty, the best alternative may be difficult to identify. Consider, for example, the problem of a delivery agent who must make 100 deliveries to different residences scattered over

Lagos metropolis. There may literally be thousands of different alternative routes the agent could choose. However, if the agent had only 3 stops to make, he/she could easily find the least-cost route.

Decision making under uncertainty is always complicated. It is the probability theory and mathematical expectations that offer tools for establishing logical

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procedures for selecting the best decision alternatives. Though statistics provides the structure for reaching the decision, the decision maker has to inject his/her intuition and knowledge of the problem into the decision-making framework to

arrive at the decision that is both theoretically justifiable and intuitively appealing.

A good theoretical framework and commonsense approach are both essential ingredients for decision making under uncertainty. To understand these concepts, consider an investor wishing to invest N100, 000 in one of three possible

investment alternatives, A, B, and C. Investment A is a Savings Plan with returns of 6 percent annual interest. Investment B is a government bond with 4.5 percent annual interest. Investments A and B involve no risks. Investment C consists of shares of mutual fund with a wide diversity of available holdings from the securities market. The annual return from an investment in C depends on the uncertain behaviour of the mutual fund under varying economic conditions.

The investors available actions (ai; I = 1, 2, 3, 4) are as follows a1: do not invest

a2: select investment A the 6% bank savings plan.

a3: select investment B, the 4.5 % government bond.

a4: select investment C, the uncertain mutual fund Observe that actions a1 to a3 do not involve uncertainty as the outcomes associated with them do not depend on uncertain market conditions.

Observe also that action a 2 dominates actions a1 and a3. In addition, action a1 is clearly inferior to the risk-free positive growth investment alternatives a2 and a3 as it provides for no growth of the principal amount.

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Action a4 is associated with an uncertain outcome that, depending on the state of the economy, may produce either a negative return or a positive return. Thus there

exists no apparent dominance relationship between action a4 and action a2, the best among the actions involving no uncertainty.

Suppose the investor believes that if the market is down in the next year, an investment in the mutual fund would lose 10 percent returns; if the market stays the same, the investment would stay the same; and if the market is up, the

investment would gain 20 percent returns. The investor has thus defined the states of nature for his/her investment decision-making problem as follows:

s1: the market is down.

s2: the market remains unchanged.

s3: the market is up.

A study of the market combined with economic expectations for the coming year

may lead the investor to attach subjective probabilities of 0.25, 0.25, and 0.50, respectively, the states of nature, s1, s2, and s3. The major question is then, how

can the investor use the foregoing information regarding investments A, B, and C, and the expected market behaviour serves as an aid in selecting the investment that

best satisfies his/her objectives? This question will be considered in the sections that follow.