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In this assignment, we will attempt to study the effects that difference in Income Ratio (henceforth known as I.R.) between the years 1980 and 1990 have on the Productivity Growth (P.G.) during the same period of time.

The Income Ratio of one specific year can be found if we take the average income of the richest faction of a country (the richest 20% of the population) and divide it by that of the poorest faction (the poorest 20%). In this assignment, the Income Ratios that were used were those of 13 different countries. The I.R.'s on both 1980 and 1990 were taken for all these countries and, to find the difference between them, the I.R. for 1990 was divided by the I.R. for 1980, for each country. These new numbers illustrate the change of I.R. between the two years so that we can compare how the P.G. changes in relation to the changes in the I.R..

On this assignment, we use inductive reasoning to examine the data and find a theory (a hypothesis) that would combine the data given in a way that would make sense, based solely on our data. How do we know if the "theory" that we formulate makes sense? In this case we will plot the points (derived from the column "I.R. 1990/1980," going on the x-axis, and the column "Productivity Growth 79-90," on the y-axis). According to how the points are on the graph in relation to the Average Point (0.94,1.45) (point that is an average of all values and which divides the graph into four Quadrants), if 80% of these points are where they would be expected to be to conform to the hypothesis, then there is no reason to reject this hypothesis. If, on the other hand, the majority of the points does not conform to our hypothesis (are not where they were predicted to be), then it is rejected.

Another method of reasoning frequently used by Mainstream economists is "deductive knowledge," as opposed to "inductive," described above. Their theory is formulated and only then it is applied to the data. Their theory on this subject suggests that productivity within a country grows when the population has incentives to work harder (or to work more). When the gap between rich and poor increases (an increase in I.R. form 1980-90, resulting in a larger ratio on the column I.R. 1990/1980), so does the population's eagerness to work, therefore increasing the Productivity Growth. Since when one variable goes up the other also goes up, there is a positive (or direct) correlation between the two. Mainstream economists use deductive reasoning to deduce that there exists a positive correlation between the two factors. In short, their hypothesis is that when the Income Ratio increases, the Productivity Growth also increases, since people are more motivated. For this to be true, we would expect a line going up and to the right on the graph, passing by Quadrants II and IV. Most points (80% or more) would have to be on these two Quadrants. This, however, is not the case (see graph), since only about 30.77% of the points plotted satisfy these conditions.

Since the original hypothesis was rejected, we might want to see if there is a negative correlation between the two variables (that is, as one goes up, the other goes down). Our new hypothesis would then be "as the Income Ratio increases, the Productivity Growth decreases." Then, in the case of a high I.R., people in lower classes would rationally start to feel insecure and that their work is not being recognized by society, therefore losing motivation and producing less. In this case, since there's a negative correlation, one would expect the line on the graph to go downwards, from left to right, passing on Quadrants I and III. If this hypothesis were valid, 80%+ of the points would have to be on these Quadrants. This is also not the case, for only 69.32% of the points are on the appropriate Quadrants. Like the first, this second hypothesis also has to be rejected.

After analyzing these two relationships and seeing that neither is valid, we conclude that there is no direct relationship between the two variables tested. That does not mean that one has no effect on the other (it probably does), only that there may be other factors and influences involved that have not