The core of managerial economics historically has been the application of marginal analysis to determine optimal solutions for specific managerial problems. Marginal analysis, and its related theory of the firm, have roots deep in the mathematical calculus. The basic concept, however, can be explained readily in nonmathematical terms.
The essential notion underlying all marginal analysis is that the search for an optimum or best possible position can be attained by trading, at the margin, one small additional quantity for another. Thus, assume that we want to maximize net revenues, what we called “net income after taxes (earnings)”. To do this for one given product, the business manager should continually compare the additional sales and revenues and costs he realizes or incurs by making small changes in the product’s output level. As long as small increases in output add more to the firm’s revenues than to its costs, marginal revenues can be said to be greater than marginal costs and additional units of output can be seen to be profitable.
Similarly, should labor or capital resources be transferred from the production of one good to another, marginal additions to revenue from the second good must be offset against marginal losses in revenue from the first. Should the additions be larger than the transfer is to increase the firm’s profitability. Similarly, should small amounts of one resource (such as capital) be substituted for small amounts of another (such as labor) to produce the same level of output, the additional costs incurred by increasing one’s use of the first resource must be offset against costs saved by reducing the use of the second. Again, should the cost savings be greater than the cost increases “at the margin,” the transfer will be profitable and presumably desirable; if not, the transfer should not be undertaken.
In general, marginal comparisons as these are not limited to specific, discrete choice at particular levels of output or specific resource combinations. Rather they are pursued continuously until all favorable transfers or tradeoffs have been adopted and optimal output levels or resource combinations have been obtained. For example, if a product’ marginal revenue is greater than its marginal cost at a particular level of output and a production increase is profitable, then a further increase at the new margin may be desirable, and again at a still higher output level, until finally, marginal revenue no longer exceeds marginal cost and further increases in output no longer add to the firm’s profitability.
One could, if he wished, visualize this decision process of trading at the margin as resembling that adopted by a myopic mountain climber (say Mr. Magoo) who doesn’t know precisely where or how far away the top of the hill (the optimum) may be and does not care. He is confident, however, that as long as he goes uphill, he will eventually get to the summit. For the business manager, the hill’s height is measured in units of profit rather than distance above sea level; its gradient is called marginal profit (which, in turn, is the difference between marginal cost). As long as marginal revenue is greater than marginal cost, of course, their difference
marginal profit = marginal revenue – marginal cost
is positive, and the course of action of our myopic decision maker is well defined—output should be increased. When finally he reaches the summit there is, of course, no place else to go. His profit gradient is zero; marginal cost and marginal revenue are identically equal to each other (by definition), and an optimum output level has been obtained.
The basic concept is very simple and very general. However, in rough terrain containing more than one peak, or local optimum, it is potentially misleading. Then one faces the problem of deciding whether one is at the highest of attainable summits or just on top of a foothill. Fortunately, there are simple mathematical tests for making this determination. But they need not detain us here.
For our present purposes, it is necessary to note only that the marginal or incremental evaluations provide us with a decision rule for evaluating the possible tradeoffs available to a firm between different courses of action. As long as the marginal relationships between different tradeoffs are not equal to one another, it benefits a firm to make some changes. Thus, if one additional unit of output increases costs, it pays the firm to increase its level of output. Similarly, if the wage costs associated with an increase in labor inputs are less than the capital costs required to increase to increase output by an identical amount, it pays the firm to use more labor and less capital to achieve any increase in production. Or if marginal revenues obtained per unit of cost from one product are greater than those obtained from another, it pays the firm to transfer resources from the production of one good to the other. At the margin, therefore, a firm’s operations are optimally balanced only when such favorable tradeoffs no longer exist, that is, when these marginal tradeoffs are equalized all around.
The key terms, then, are tradeoffs and equalization of margins. And the purpose, stated once again, is to achieve an optimum, either in the form of maximum net profits or minimum costs. To develop these marginal concepts further, we shall next consider two illustrative applications commonly encountered in business: the pricing decision and inventory management.
Conclusion
The uses of marginal analysis in business problem solving are hardly exhausted by the illustrative pricing and inventory problems. Indeed, the basic concepts of marginal analysis underlie almost all optimization procedures used by managerial economists or operation researchers today.
