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Marginal Analysis for Optimal Decisions

In this chapter we have given you the key to the kingdom of economic decision making: marginal analysis. Virtually all of microeconomics involves solutions to optimization problems. The most interesting and challenging problems facing a manager involve trying either to maximize or to minimize particular objective functions. Regardless of whether the optimization involves maximization or minimization, or constrained or unconstrained choice variables, all optimization problems are solved by using marginal analysis. No other tool in managerial economics is more powerful than the ability to attack problems by using the logic of marginal analysis.

The results of this chapter fall neatly into two categories: the solution to unconstrained and the solution to constrained optimization problems. When the values of the choice variables are not restricted by constraints such as limited income, limited expenditures, or limited time, the optimization problem is said to be unconstrained. Unconstrained maximization problems can be solved by following this simple rule: To maximize net benefit, increase or decrease the level of activity until the marginal benefit from the activity equals the marginal cost of the activity:

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When the choice variable is not continuous but discrete, it may not be possible to precisely equate benefit and cost at the margin. For discrete choice variables, the decision maker simply carries out the activity up to the point where any further increases in the activity result in marginal cost exceeding marginal benefit.

Marginal analysis shows clearly why decision makers should ignore average costs, fixed costs, and sunk costs when making decisions about the optimal level of activities. Since it is marginal cost that must equal marginal benefit to reach the optimal level of activity, any other cost is irrelevant for making decisions about how much of an activity to undertake.

In many instances, managers face limitations on the range of values that the choice variables can take. For example, budgets may limit the amount of labor and capital managers may purchase. Time constraints may limit the number of hours managers can allocate to certain activities. Such constraints are common and require modifying the solution to optimization problems. To maximize or minimize an objective function subject to a constraint, the ratios of the marginal benefit to price must be equal for all activities,

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and the values of the choice variables must meet the constraint.

The two decision rules presented in this chapter will be used throughout this text. If you remember these rules, economic analysis will be clear and straightforward. These two rules, although simple, are the essential tools for making economic decisions. And, as the rules emphasize, marginal changes are the keys to optimization decisions.

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