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This mathematical function is given as follows:
U = f( x1, x2, . . . xn)
This equation can also be represented in the form of a table. This table would be the map to consumer preferences. But there are two issues in this kind of table.
The first one is that there is assumption for the independence between the goods that is actually unlikely to happen. The utility of the additional goods being used depends on the number of the same good that was used earlier. It does not depend upon the number of the other things that were bought. If the goods in question are related to each other, either substitutes or complements, then there is no chance for the independence factor to exist at all. But tables should be made keeping in mind this issue and avoiding this problem of independence.
The second issue is a little more serious than that of the first one. This is one reasons that the economists avoid the tables altogether. This is true in case of the utility theory. it is assumed that a table with number would easily bring out the utility as the goals accomplishes is what measures the utility. But this is not true. This problem is overcome by means of graphs that are plotter. This would be the appropriate solution to this issue.
The Utility Maps
At the very first go, we may feel that graphs are not a good idea when compared to the tables. But when you keep using them, you will come to know that they are far better than the tables. In case you are discussing about the maximization of utilities, then you will need three variables. These three variables would be the quantity of good A, the quantity of good B and the third variable would be the level of utility. There are only two axes in the graphs, but you may need a three dimensional thing for the three variables. But there is a solution to this too. It would be similar to the way of depicting the altitude in the maps, which show the three variables as longitude, latitude and the altitude. A similar method would be used in the utility maps too. There is a line that connects all the combinations that are possible in the map. This is called as the Isoutility line or the indifference curve.