If the origin point represents our actor then each vector is a unique goal that they pursue.
Oranges = [2,2]
Apples = [-4,-1]
Bananas = [-1,2]
The sum of the vectors represents the amalgamation of the preferences, constraints, and goals of the actor. Their resultant behavior.
Sum = [-3,3]
Another person with different valuations will have this graph.
Oranges = [-6,4]
Apples = [1,1]
Bananas = [2,-2]
The sum, however, is the exact same.
Sum = [-3,3]
From the outside, all that we can see is the sum as expressed by the action of the individual. This is all that appears in aggregated data. From the perspective inside the mind, the individual can see each vector. If new goals developed or new means were discovered. We would have no way of knowing how each of these two actors would respond from merely analyzing present behavior. Human behavior is rational in the sense that we have commonly understandable concepts about it (in this case represented by vector addition). The mind locks up particular knowledge of time and place.
In “Shadow Economies: Size, Causes, and Consequences”, while discussing empirical studies of the shadow economy (underground wheelings and dealings that don’t get counted in official GDP Tony Soprano, crime, untaxed labor etc.), two findings are noted. The first is that increases in the marginal income tax rate are positively correlated with the size of the shadow economy. Second,
A country with high tax rates and effective bureaucracy or a country with low tax rates and ineffective bureaucracy might show the same behavior in terms of shadow economy activity. Both economies would react differently with respect to different changes. If we only go by empirics here, we cannot tell which country requires which policy. We require a conceptual dimension of economic science to understand what is going on inside each economy. To know which move to recommend
Behavior doesn’t reveal preferences; in many ways it clouds them.
Citation: Schneider, Friedrich, and Dominik H. Enste. “Shadow Economies: Size, Causes, and Consequences.” Journal of Economic Literature 38, no. 1 (2000): 77-114. http://www.jstor.org/stable/2565360.