Use of Simphfled Models: Theory

The most apparent fact about economic re- ality is its complexity. There are millions of busi- nesses, 200 million consumers, hundreds of thousands of different products, multiple stages in the production of nearly every product. Faced -~ with this overwhelming complexity, we obviously have to find some way of simplifying things down to manageable proportions. The first job is to simplify.

In order to do so, the economist, like other scientists, begins by developing an analytical framework, or model, of the reality he wants to analyze. This model focuses on the main elements and main relationships in the complex real eco- nomic world he is studying. For example, in the tax case above the main elements of the model were consumer behavior, business behavior in re- sponse to increased demand, and the respending cycle in response to the original increase in dis- posable incomes.

Such simplified models are often called “theories.” They make no pretense of being accu- rate descriptions of any part of the economy. If they were completely accurate they would defeat their own purpose by getting back to all the de- tail. Instead, they are intended as highly simplified abstractions of the main elements of the reality to which they apply.

The notion of a model, or theory, may be illustrated by a noneconomic example. Suppose you want to understand how a bicycle works—a theory of its operation. You could study every de- tail of a single bicycle, or a large number of them, examining the tires, the handlebars, the sprocket, the paint, and so on. But if you could instead get a simple diagram, or a stripped-down working model of a bicycle, you’d get to the essentials quicker. This diagram wouldn’t be concerned with all the details of paint, style, quality of steel, and so on. Instead, it would show the fundamental parts of the bicycle—wheels, frame, sprockets, driving chain, brake—and the basic relationships among these parts. The diagram would show how foot pressure applied to the pedals turns the sprocket wheel; how the chain connects this large sprocket to a smaller one at the center of the back wheel of the bicycle; and how, because of the dif- ference in the size of the sprocket wheels, pressure on the foot pedal exerts a multiplied pressure in turning the back wheel. The diagram should also indicate the important numerical relationships, for example, between the sizes of the large and small sprockets of the pedal and the back wheel.1 People have used such a model of a bicycle many times, and its predictions have been thoroughly validated by empirical evidence. The theory, or model, is thus a good one in that it helps us to understand the way a bicycle works and to predict the conse- quences of changing the main variables—for exam- ple, the sizes of the two sprocket wheels. The theory “works.”

So it is in economics. A model is a simplified diagram indicating the main elements in any situa- tion, and the main interactions among these elements. The more firmly validated these rela- tionships are by empirical observation of many cases, the safer we feel in using them in our model. Some models are very sketchy, merely identifying the main elements and loosely stating their inter- relationships. Others specify precisely the rela- tionships connecting the main variables, as when specific physical principles are used in explaining the operation of a bicycle. Unless we are reason- ably precise as to the main economic forces at work and their interactions, with empirically vali- dated quantitative statements of these relation- ships, we cannot safely predict how the economy will react to particular events or policy measures like the tax cut.

An economic model may be stated as a dia- gram, and many graphs are used in the pages ahead. It may be stated in words, as in the bicycle case; this will be done many times. Or it may be stated in mathematical terms, but except for a little simple algebra and geometry used in the dia- grams, we shall use little mathematics.2 Most economic models can be stated in any of these three ways.

Last, it is important to emphasize that the economist doesn’t apologize for the fact that his theories don’t describe the real world precisely and in detail. On the contrary, like any other scientist, he says that any theory is a skeleton, or a frame- work, to help simplify and understand the intri- cate complexity he is attempting to understand and predict.

"Other Things Equal" and "Equilibrium"

The real world is far too complex for us to analyze everything at once. Thus, in common with many other scientists, economists use the concept of holding “other things equal,” or “constant.”

In the chemistry laboratory, we hold “other things equal” through controled experiments. We put two elements (say hydrogen and oxygen) to- gether in a test tube under controled conditions, and get water if the proportions are two to one. In the bicycle example above, we hold friction, gravity, air pressure, and various other factors constant (or assume them away altogether) in analyzing the way the bicycle works. So it is in economics. To understand, say, what happens when consumers receive larger disposable incomes because of a tax cut, we may want to assume that many other things are “constant”—for example, the stock of money in the economy, political con- ditions, and the like—in order to simplify the job of analyzing the result of the tax cut. If at the same time that taxes are cut, war should break out, obviously consumers might use their addi- tional disposible income differently than under peacetime conditions. In the real world, “other factors” may not stay constant; but by assuming temporarily that they will do so, we can isolate the impact of the increased after-tax income in which we are interested.

This idea is closely related to the concept of “equilibrium,” which is also widely used by scien- tists. In chemistry, for instance, after we’ve com- bined hydrogen and oxygen to form water, this equilibrium state is maintained until something disturbs it. In the same way, economists generally think of the economic system as tending to move toward equilibrium when some disturbing change occurs; and in analyzing the movement of any sector of the economy toward equilibrium after it is disturbed, they commonly hold many “other things equal” in order to isolate the effects of the change being studied.

Consider a simple example related to the tax cut above. We may say a household (or a consumer) is in equilibrium when it spends just that proportion of its income on all different products which bring it the greatest total satisfac- tion, and saves the rest. Say the household is re- ceiving $100 per week and spending $95 on a variety of goods and services while saving $5 per week. Now its disposable income rises to $110 weekly because of the tax cut. It is now obviously out of equilibrium because, unless it increases its spending on consumer goods and services, it will be saving $15 per week, a large increase in the percentage saved. This saving increase may well occur temporarily, because it takes time to adjust to changes in our economic affairs. But the house- hold will presumably want to adjust toward a new equilibrium pattern of spending with its larger income. At the new higher level of income, it may decide to save a larger proportion of its disposable income, or it may decide that 5 per cent is still about right. Either way, once it has adjusted its spending to the desired allocation of its income among all possible uses, it is again “in equi- librium.” We mean by equilibrium a situation in which everybody is satisfied to keep on doing what he is doing. In economic equilibrium, there’s nothing at work to change the economic behavior under consideration.

To repeat, “equilibrium” and “other things equal” are purely analytical concepts. No one believes that in the real world “other things” do always stay equal when we are trying to analyze the behavior of the economy, or that economic units are always in equilibrium. Use of these con- cepts simply helps us to trace through what would happen if all “other things” in the economic sys- tem remained unchanged until the new factor under consideration (such as the tax cut) had fully worked itself out. But don’t think that this makes economic analysis just an intellectual game. Such analysis can give us powerful conclusions as to the direction the economy, or parts of it, will move in response to different individual actions or government policies, even if it can’t tell us just what the end result will be some time hence in a world of many simultaneous crosscurrents.